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KRONOS Vol V, No. 1




Professor Alexander Thom has spent the last thirty or forty years of his summer vacations patiently surveying Megalithic remains in the British Isles.

He came to three main conclusions about Megalithic stone rings. Firstly, that they were not all circular, and that those that were not were intentionally laid out in the form of other geometric figures. Some had their perimeters extended into egg-shapes, while others were squashed into flattened circles. Secondly, a common unit of length, which Thom has termed the Megalithic yard, and which is 0.83 meters long, was employed in setting out these shapes. Lastly, Thom contends that many of these stone rings and circles were associated with other stones or prominent natural features to indicate directions on the ground which would have been astronomically significant to Megalithic man. According to Thom, some of these directions pointed to the rising or setting Sun at the solstices or equinoxes, while others pointed to the rising or setting positions of the Moon at either the major or minor standstills.

In his Megalithic Sites in Britain, Thom considered that Megalithic man was only capable of approximately delineating these limiting positions of the Moon. Later, however, in a protracted article(1) and in a following book,(2) he claimed that Megalithic man was capable of detecting the tiny perturbation or wobble of the lunar orbit caused by the Sun "passing" through the lunar nodes. If Megalithic man was able to accomplish this not inconsiderable feat, he would have had to develop fairly sophisticated mensuration techniques.

This sophistication would seem much at variance with the established archaeological and anthropological model of an illiterate and innumerate society existing meagerly in a bleak and inhospitable environment. In order to circumvent this embarrassing dichotomy, Thom postulated the existence of "a school or system of mathematical reasoning" responsible for the design, construction, and operation of these lunar observing stations. This proposal has been developed by his supporters into the paradigm of Megalithic Theocracy the astronomer priesthood organising and dominating their more humble brethren. The concept of this intellectual elite is, however, somewhat peripheral to the aims of this article which is mainly concerned with the following problems:

(a) How convincing are these lunar lines from a menhir or group of menhirs to horizon features?

(b) Could Megalithic man have actually determined the lunar perturbation, given that he was interested in doing so?


Is the evidence that Thom presents of the lunar lines which supposedly run from the Megalithic remains to natural features on the horizon convincing? Can the lines be regarded as deliberate astronomical devices to help Megalithic man determine the perturbation? Are they accidental, or have they been deliberately selected with the aim of substantiating preconceived opinions?

Unfortunately, Thom has been virtually the only worker in this field. We have, therefore, to examine the reliability of these lunar lines from the information presented by Thom in his various works. In order to investigate the lunar lines as objectively as possible, the following points will be considered:

(a) What weighting would be given to the lunar lines in the context of Thom's own classification system for supposed astronomical lines?

(b) Could the lines be associated with some other astronomical body?

(c) Can precise declinations of the form (e i D S) be given to each line?

(d) Thom has shown by astronomical retrocalculation that the datings of the lines cluster together and are possibly synonymous with the archaeological datings of the monuments. This can be interpreted as evidence in support of Thom's thesis by showing the homogeneity of the lines. But how valid are Thom's dating methods?


Following Thom, the lunar sites can be differentiated into sophisticated observatories and simpler observing sites. Thom considers that the former were used to determine more than one important limiting position of the Moon, and that observing errors due to parallax and refraction variations were eliminated. Less attention has been focused on the observing sites which Thom considers to be either last remnants of observatories, or sites that could only show that the Moon happened to be at a limiting position at a standstill. Although these sites are of less importance than the observatories, they do constitute a very important element in the evidence that Thom uses to support his contentions that Megalithic man studied the perturbation, for 24 of the 40 lunar lines that Thom considers to be reliable are associated with these lesser observing sites.

By far the most common types of lunar lines are those associated either with (i) alignments of two or more stones, or with (ii) solitary menhirs.

These will be investigated in the light of Thom's own published classification and selection criteria. Thom himself tells us that:

"For the sun or moon we must have as a minimum:

  1. a long alignment,
  2. two well separated stones,
  3. a circle with an outlier some hundreds of feet distant, or
  4. a natural foresight identified by some simple indicator."

He classifies the lines as follows:

  • "Class A contains those lines which it is considered would be accepted by any unbiased observer.
  • Class B contains borderline cases which some people might accept and others discard.
  • Class C contains lines which would be excluded from a statistical analysis. For example, a line from a site to an impressive natural foresight is marked C when its only claim is that it gives one of the declinations in which we are interested."(3)

Consider firstly a row of stones (an alignment) which is oriented towards a natural horizon feature (the foresight). This line would obviously be weighted or ranked as Class A. Thom gives examples of such lines as being associated with accurate observations of the Moon at the standstills, and these appear to be significant evidence that Megalithic man did indeed study the perturbation. However, closer analysis of these alignments often casts doubt on either the validity or the accuracy of the lines. Let us, for example, take the following alignments from Thom's own Megalithic Lunar Observatories.

Duncracaig : This site consists of four slabs, two of which are 9, the others 12 and 13 feet high, arranged in a rough line. In 1965,(4) Thom himself noted the line to be poorly indicated and the stones are shown distinctly not arranged in a straight line. But by 1971,(5) we find Thom describing the site as having an impressive lunar alignment with an accompanying diagram(6) which shows the slabs as being co-linear and indicating a natural foresight at Garbh Sron. In the space of five years, the stones have apparently moved into a straight line, giving Thom his important lunar sighting.

Escart : Thom considers this an impressive alignment.(7) But this line suffers from the fact that a wall divides the alignment in two besides having the line to the horizon obscured by shrubs and trees. Additionally, the observer is required to stand at the north end of the alignment and look down towards the smallest stone. As the most northerly slab is 11 feet high, this would indeed be difficult.

Stillaig : In 1969,(8) the horizon profile(9) could not be regarded as being accurate by the standard that now seems necessary for lunar sites. But we notice that, by 1971,(10) the same profile is said to be only "inaccurate by a minute".

Parc-y-Meirw : In 1971, Thom stated that "this alignment of four large menhirs is undoubtedly lunar".(11) He believes that a line from this alignment indicated a small hill just north of Black Rock Mountain (called Black Mount by Thom). However, this line could not have been used because this small hill would not have been visible from Parc-y-Meirw except under freak atmospheric conditions. This has nothing to do with the exceptional clarity that Thom claims for the Megalithic era but is simply due to the dip of the horizon. It is singularly revealing to discover how Thom arrived at the conclusion that Parc-y-Meirw was a reliable lunar alignment. His first mention of this alignment was in 1966 when he stated that the horizon was very near.(12) In 1967 he contended that it was possible "at least in theory to see the Irish Hills''(13) from Parc-y-Meirw. By 1969 Thom, in his profile of the Black Mount area, incorporates a small hill (called A) just to the right (or north) of Black Mount, and makes the interesting observation regarding its visibility: "Calculation based on the original O. S. of Ireland showed that in fact Mount Leinster is in sight but the large distances involved (over 90 miles) makes the refraction very uncertain. The hill Croaghaun probably shows but the small hill to the right (A) would be very low unless the refraction was higher than we were using." (14) But Thom on his own admission is already using higher than generally accepted values of refraction.(15)

In his final profile in 1971,(16) Mount Leinster (the highest peak in the area and just left of Black Mount) is now 10' above the horizon as opposed to 8'in the 1967 figure;(17) and Thom now reflects that "in our present state of knowledge it is unsafe to assume that Croaghan would have been visible on the Moon's disc but it seems reasonable to assume that point A was normally visible".(18) A most interesting reversal. The question to be asked is whether point A would have been visible from Parc-y-Meirw, and this is easily resolved.

There are standard formulae, which vary depending on corrections for refraction effects, used for calculating the furthest distance seen on the horizon from a given height. The formula used here employs a large refraction correction. Thus we will give Thom the benefit of the doubt concerning visibility of the Irish Hills from Parc-y-Meirw. We wish to find the minimum height or altitude (H) that could be observed 91 miles from Parc-y-Meirw (altitude 649 ft.). For the intervisibility of the two heights as we have here (H and 649 ft.), the horizon distances are calculated separately for each height and then added. The formula employed is L = 1.323 SQRT(D) where L is the distance seen in miles on the horizon and D is the height in feet of the observer's position above sea level. So 91 = 1.323 SQRT(649) + 1.323 SQRT(H); so H = 1850 ft. It would seem that even using high refraction values any point under 1850 ft. would not be visible from Parc-y-Meirw even under conditions of utmost atmospheric clarity.

Mt. Leinster (2610 ft.) and Black Mount (1975 ft.), on the clearest of days, could both be conceivably visible from Parc-y-Meirw. But inspection of Thom's horizon profile shows A well below these two heights, so A would be invisible. An inspection of the most accurate map I could find of the area Irish Ordnance Survey (Suirbheireacht Ordanais) Scale 1/2 ins. to a mile, No. 19 shows the small hill A falling steeply into the river Clody. Its altitude as read from this map is much less than 1850 ft.

Unless refraction effects in the Megalithic era were somehow much greater than at present, the line from Parc-y-Meirw to point A would have been untenable. Conversely, if they were great enough to make point A visible from Parc-y-Meirw then the rest of Thom's horizon profiles would have to be regarded as invalid.

The other type of lunar line associated with alignments is that obtained from the alignment itself, as no foresight is evident. Thom

gives two examples of such a line:

Corogle Burn (Glen Prosen) : In 1965(19) Thom presented a plan of this alignment which shows four stones in a line. At the north end, two smaller stones are about 20 feet apart, but two larger ones at the south end are indicated as being in a fallen state. In his 1971 plan,(20) Thom omitted to indicate that the two large stones at the south end were prone. Lines running through fallen stones are less than desirable if accuracy is what one wishes to emphasize. The accuracy of this line must therefore be somewhat lower than that which Thom assigns to it.

Kell Burn : Here, again, Thom exhibits his inconsistency. In 1969, Thom stated that the azimuth from the alignment "ought to be reasonably accurate". Whereas, by 1971, he assured his readers that it gives a "fairly accurate azimuth".(21) If we now consider lines associated with solitary menhirs, which are irregular, we find that they appear to have no astronomical significance. Irregular menhirs, by implication, are not oriented towards any particular horizon feature. In an environment with a suitable notchy and broken horizon, the type common to the locations where most of Thom's lunar sites are to be found, it would not be difficult to find one line taken from the stone to a natural feature on the horizon that would indicate some important astronomical occurrence. Thom has stated that:

"When we find even ... an isolated stone, we ought to look round the horizon. If there is a suitable natural foresight which gives a commonly found solar or lunar declination exactly, then we are entitled to suspect that there may have been a secondary indicator which would have identified the foresight but that it has vanished. Such a line could only be given a low classification and would not be put on a general histogram."(22)

This is, to some extent, reasonable; but one should always work with the evidence found on the ground and not with what one would like to find. Consider another of Thom's statements regarding the importance of lunar markers:

"When we understand that years of work went into finding an exact spot where a backsight should be placed, we begin to appreciate why it was important to mark the spot well and permanently."(23)

Objective criteria would suggest, and Thom would agree, that the minimum requirement of a backsight is that it should indicate the natural feature which acts as the foresight. If a solitary menhir was used as a backsight, we would expect that it would be hewn, even if roughly, to a regular shape, i.e. some sort of a slab, and that the faces (or even edges) of such slabs should indicate the foresight. Even a partisan supporter of Thom, J. E. Wood, was forced to conclude that:

"There are many sites with only a single megalith and where the shape of the stone provides no guide to the direction of the distant foresight. There is always doubt about isolated stones as possible markers being for astronomical purposes, since they could have other uses such as boundary stones."(24)

Those lunar lines associated with irregular menhirs would merit class C weighting and must therefore be disregarded as evidence that Megalithic man studied the lunar perturbation.

Another type of line is that obtained from a single menhir with flat faces which could be positioned to indicate a natural foresight. Thom presents examples of lines associated with this type of shaped stones but even here careful analysis shows that they, also, have little, if any, astronomical significance. A few examples follow:

Knockstaple : This site consists of a large slab which gives a reliable azimuth, but no foresight is indicated, and Thom rates this line as having little precision.

Camus an Stacca : Here we have a large slab with a definite azimuth but no evident foresight.

Bunessan : The shaped slab here can be said to be oriented to a boulder on the horizon but Thom himself was unable to attach any weight to the indicated line.

Leacach an Tigh Chloiche : In 1967, Thom described this site as a mixture of open kists and upright stones.

"The sketch plan [included in Thom's work] shows how the large menhir at Leacach an Tigh Chloiche points roughly in the direction of Wiay . . . The moon in its mean most southerly position is shown rising behind Ben Tuath."(25)

Of this site, as of two others in the Hebrides, Thom states that it shows "not only the lunar declination but the declination limits correct to a minute or so"(26) (Emphasis added).

However, by 1969, Thom seems to have had a change of mind. Consider his words:

"The indication of the lunar line is weak consisting of only a single slab. The declination limits are wider than we would expect being 25' instead of 19' but the profile is not of high accuracy"(27) (Emphasis added).

Knockrome : Here there is a line of three widely separated stones. Thom tells us that "the orientation of the centre stone draws attention to Crackaig Hill".(28) But is the line of stones an alignment? It would seem that if Megalithic man had gone to the trouble of erecting three stones at a lunar site, he would have lined the three stones in a row so that they would indicate the foresight.

Evan Hadingham, who conducted similar surveys of Megalithic remains in the west of Scotland, gives us this important comment:

"A reading of Thom (1971) would suggest that most isolated standing stones with flat faces should indicate distant natural features for precise astronomical observation. Out of seven such sites investigated, five showed elevated and very close horizons (some within a 1/4 mile) . . . More often than not, there were too many notches on the horizon to be distinguished by the face of the stone.

"The tendency for stones to be near the meridian, taken with the proximity of most of the horizon, might be considered to make 'super precise' astronomical explanations both unnecessary and unlikely."(29)

A large sample of Thom's lunar lines has been subjected to detailed scrutiny and many of the lines can be dismissed as having negligible astronomical significance. The lines associated with solitary menhirs have little credibility while those connected with alignments are far from impressive. If one takes into account the work of Jon Patrick at Temple Wood,(30) which casts considerable doubt on the role of this particular site as a lunar observatory, and also the resurveying done by Cooke et al. at Callenish, (31) where all but one of the supposed astronomical lines are regarded as erroneous (and that solitary line has a high probability of being accidental), little seems to remain of the seemingly impressive edifice that Thom erected in support of his contentions that Megalithic man studied the perturbation. (It may be mentioned in passing that selection of many of these lines seems to have been based on purely subjective criteria while, in several cases, the data appears to have been approached in such a way as to accommodate the evidence to the hypotheses being presented.)


If we accept the premise that Megalithic man did indeed study the motions of various heavenly bodies, can we be sure that all the sites presented in Thom's Megalithic Lunar Observatories are indubitably lunar, or could they possibly be identified with other astronomical bodies? Is Thom justified in adjusting all of these declinations by the order of 50' in order that the revised figures correspond with the declinations he requires for the viability of his lunar hypotheses?

The histogram of observed declinations published by Thom in 1967 (32) shows that declinations agreeing with two of the four important limiting lunar positions would also correlate with stellar declinations. One at a minor standstill (28 ) could be associated with both Sirius, the brightest of all stars, and Rigel. Thom states that "Sirius has no indicators but with Orion's belt to show where it would rise or set no identification would be necessary".(33) But, in the absence of oral or written traditions concerning the function of these stones, how does one differentiate among the Moon, Sirius, and Rigel? The other declination is assigned to a major standstill (28) and is slightly less than the tabulated values for Castor for the period 2000-1500 B.C. However, more recent datings for the erection of the megaliths place them between 3000-1500 B.C. As one would expect stellar observations to have preceded the more sophisticated lunar measurements, Castor would have similar rising and setting positions as the Moon at this standstill.

Thom circumvents this problem by assuming that lunar sites, as mentioned previously, are associated with backsights in the form of either very tall stones or impressive alignments. He considers that these should be judged as the criteria for such sites. Distinctive menhirs, however, were used, according to Thom, to indicate other astronomical bodies. Both Clach an Trushel,(34) the largest standing stone in Scotland, and another impressive menhir, Clach Mhor a Che,(35) seem, according to Thom, to be oriented towards the star Altair. In this context, solitary menhirs are taken by Thom to indicate his calendrical declinations which are without doubt the weakest of Thom's astronomical assertions and, as important stellar declinations coincide to a great extent with these same declinations, how are they distinguished? Again, impressive alignments are certainly not the prerogative of lunar sites, even according to Thom, as notice the non-lunar attribution of those at Saeth Maen, Rhosygelynnen, Knockrome, Ballochroy, Nine Maidens, Eleven Shearers, etc.

There do not appear to be any reliable criteria in operation for choosing which particular body is to be selected when the declinations are similar. At Temple Wood, Thom has changed a line initially given by him for Castor to the Moon. It would therefore seem that the adjustment of many declinations to account for lunar parallax is necessarily subjective.


In a table,(36) Thom gathers together his reliable lunar lines and assigns to each line a definitive declination of the form (e i D S) where e is the obliquity of the ecliptic, i is the inclination of the lunar orbit to the ecliptic, D is the amplitude of the perturbation, and S is the mean lunar semidiameter (where e, i, and D refer to the centre of the Moon's disc). Declination is thus treated as a function of the observer's latitude, the azimuth of the line from the observer to the foresight, and also the altitude of the Moon to the observer. The first two terms are easily obtained, but the estimation of the apparent altitude is beset with great difficulties. Thom himself acknowledges that "if they [the corrections] were not made, any analysis of the lunar declinations obtained would be meaningless".(37)

The corrections are for refraction both astronomical, in which the light from the Moon through its total atmospheric path is curved, and terrestrial, in which the light is bent between the foresight and the observer.

In order to arrive at the altitude, the horizon profile is measured in daytime conditions, and corrected to night-time conditions by allowing for the different temperatures and, therefore, refraction effects then prevailing. However, the night-time conditions should be those for Megalithic times and, accordingly, some assumptions must be made about such conditions. Parallax variations of about +4' must also be taken into account.

For observations near the horizon, the change in declination Dd produced by a small change in altitude Dh is given by Dd = (sinf/cosd) Dh where f is the latitude, d the declination. For a latitude of 55 and a declination of 30, a change in altitude of 1' will cause the declination to vary by about 55", so altitude changes are critical considering that the perturbation amplitude is 9', and the mean semi-diameter is 15'. Thom may be too sanguine when he gives his lines precise declinations of the form (e i D S) because the difference between the limits (+D+S) and (-D-S) is only 48' and there are nine possible lines that can be placed between these limits.

Interestingly enough, Thom gives no worked examples of a calculated lunar horizon profile but does give profiles for solar lines. Correction effects for the latter are much easier to estimate and are much less prone to error, while parallax changes can be ignored. Refraction corrections for six solar lines are given in one of Thom's tables(38) and these vary between 21.5 and 35.5 minutes. It would be most interesting to see the range for lunar lines.

It must be suspected that, although Thom spent much time and effort in measuring refraction effects, there must be a certain degree of doubt attached to both the calculated declinations and the definitive value of declination assigned to each line.

Another limitation to putting definite declinations on lines is noted with regard to many of the observing sites. Thom considers that the observing sites may well be the last remnants of former observatories. Yet he himself states that:

"Some are so placed that it is difficult to see how any station did any more than show on a certain date that the moon happened to be at one of its limiting positions when it rose or set on a foresight."(39)

If no extrapolation techniques were available, then the value of the declination obtainedcould not be of the form (e i D S).

Figures 1, 2, and 3 show the maximum monthly declinations (MMDs) over the last three standstill periods together with the declinations obtained at the two nearest moonsets to each MMD, for a position of latitude 52 and longitude 0. If we assume that the differences between the MMD and the moonset declinations would be fairly representative of those in Megalithic times, and if refraction and parallax errors are taken into account, it is easily seen that all one can say with regard to a lunar line obtained from a site where no extrapolation was possible is that it may have shown the approximate limiting position of the Moon.

This is shown by considering that the maximum geocentric declination possible is (e i D S). For a southern line this would be the lower limb of the Moon, by altitude, grazing the foresight at the limit of the perturbation. Over the last fifty years this value would be 28 59', assuming a mean semi-diameter of 15'. On only twelve occasions at the last three standstills would the moonset declination be within 9' of this value. The number of moonsets that can be utilized for any particular line is much less than half, and, taking into account observer errors due to refraction and parallax variations, can one state with any assurance that a line obtained from such a site would correspond to the specific declination Thom gives it? When lines with declinations less than the maximum are considered, the position becomes even more confused.

To conclude, there is some doubt attached to giving lunar lines definite declinations of the form (e i D S) due to the difficulty of accurately determining the apparent horizon profiles for these lines; but, even worse, to specify definite declinations for lines obtained from sites where no extrapolation techniques are possible is, obviously, an arbitrary and subjective judgement.


If it is accepted that archaeo-astronomical sites can be dated by astronomical retrocalculation, and if Thom's lunar lines are deliberate, it would be expected that the dates for these should cluster together in time and that there should be good agreement between these dates and those obtained for the megalithic remains by archaeological methods.

Thom's first attempt at dating was concerned with stellar lines. In 1955 he showed that certain alignments were consistent with the theory of stellar lines at about 2000 B.C. This date seemed rather early by the archaeological evidence of the time. Significantly, his dates for solar and lunar lines published since 1955 have moved forward in time. However, authoritative redatings of the megalithic monuments have subsequently dated the erection of these sites to between c.2800 and 1500 B.C. In view of this, Thom's dates now become rather late.(40)

Thom's dates for his lunar lines show a mean time of 1650 100 B.C. and a definite clustering together in time, which may be interpreted as evidence in support of his lunar hypothesis. But how valid are Thom's dates? Astronomical retrocalculation depends on using the very small change in the obliquity of the ecliptic which is assumed by orthodoxy to be about 40 arc seconds per century in the Megalithic era. Thom finds a mean value for the obliquity from a numerical analysis of his 40 lunar lines and, using de Sitter's formula for the change in the obliquity with time, he arrives at a mean date for these lines.

Unfortunately for Thom, this mean value depends on the accuracy of the declinations of his lines and, as has been shown, there must be a great deal of doubt attached both to the apparent altitudes from which the declinations are calculated and to the definitive declination assigned to many of the lines. Thom's numerical analysis is built on shaky foundations and the evidence of the clustering of dates for his lunar lines is rather tenuous.

This conclusion is supported when one considers that Thom has stated with regard to astronomical retrocalculation:

"Since this [the obliquity of the ecliptic (e)] changes very slowly, it seems at first sight that this method is incapable of any accuracy."

However, he concludes:

"That if we hope to determine the mean date of the erection of the sites to within a century, we must find from the sight lines values of e with a precision greater than an arc minute."(41)

But this is virtually an impossibility with lunar lines. When Thom does find anomalies in his dating methods, as for example with Temple Wood which is dated to 1700 B.C., he states:

"The accuracies of the determinations are not nearly sufficient to warrant saying that Temple Wood is necessarily earlier than the other sites."(42)

Another serious worker in the field, Professor Gerald Hawkins, considers that sites should not be dated by astronomical means as the dates can be off by as much as two thousand years.(43)

. . . to be continued.


1. Vistas in Astronomy, 11, (1969).
2. A. Thom, Megalithic Lunar Observatories (henceforth MLO), (Oxford, 1971).
3. Idem, Megalithic sites in Britain (henceforth MSB), (Oxford, 1967), pp.94-96.
4. Vistas in Astronomy, 7 (1965), p.9, fig.6, p.21.
5. MLO, p.52.
6. Ibid., p.52, fig.5.3
7. Ibid., p.59.
8. Vistas in Astronomy, 11, (1969), p.11.
9. Ibid., fig.11, p.12.
10. MLO, p.66, fig.6.11.
11. Ibid., p.73.
12. Vistas in Astronomy, 7 (1966), p.45, fig.33.
13. MSB (1967), p.159.
14. Vistas in Astronomy, 11 (1969), pp.15-16, fig.16 on p.16.
15. Ibid., p.5.
16. MLO (1971), p.73, fig.6.19.
17. MSB, p.157, fig.12.17.
18. MLO, p.74.
19. Vistas in Astronomy, 7 (1965), fig.20, p.34.
20. MLO, p.71, fig.6.16.
21. Ibid., p.70.
22. MSB, p.94.
23. MLO, p.12.
24. J.E. Wood, Sun, Moon and Standing Stones (Oxford, 1978), p.106.
25. MSB, p.131.
26. Ibid., p.132.
27. Vistas in Astronomy, 11 (1969), p.13.
28. MLO, p.65.
29. Irish Arch. Res. Forum, ll, (2), (1975), pp.9-14.
30. "Ceremonial Science and Society in Prehistoric Britain," unpublished, read at the Glasgow Conference, Sept.20, 1975; "Megalithic Astronomy - Fact or Fiction," Q.Jl.R. Astro. Soc., 18 (1977), pp.453-458.
31. Journal for the History of Astronomy, 8 (1977), pp.113-33.
32. MSB, p.102.
33. Ibid., p.105.
34. Ibid., p.129.
35. Ibid., p.130.
36. MLO, p.76, table 7.1.
37. Ibid., p.28.
38. Ibid., p.42, table 4.1.
39. Ibid., p.59.
40. C. Renfrew, Before Civilisation (London, 1973); A. Burl, "Dating the Stone Circles," in American Scientist (March 1973), p.167.
41. MLO, pp.15-16.
42. Ibid., p.79.
43. G. Hawkins, "The Place of Astronomy in the Ancient World," in Philosophical Transactions of the Royal Society of London, 276 (1974).

Acknowledgements: I have received help, advice and criticism from different quarters during the preparation and writing of the various drafts of this paper. R. J. Livesy helped greatly on astronomical matters and Dr. D. C. Heggie made a scholarly criticism of the work at all its stages. In addition I wish to thank the KRONOS staff, particularly Ray Vaughan and Dwardu Cardona for excellent proofreading and editorial work. I also wish to acknowledge the help and encouragement received from colleagues at Cardonald College, in particular James Mooney, Thomas Phalan, Allan W. McAneny, and William R. Hutchison of the Art Department in the preparation of drawings. Finally this paper benefited greatly from the constant help and advice freely given by A. J. Hastie.

[*!* Image] Figure 1. The MMDs are plotted for each lunar month. The declinations at the two nearest Moonsets are also plotted. Verticle lines therefore indicate Extrapolation Declination required. [Labels: NORTHERN (+) MAXIMUM MONTHLY DECLINATIONS. SOUTHERN (-) MAXIMUM MONTHLY DECLINATIONS. DATES OF MAXIMUM MONTHLY DECLINATION.]

[*!* Image] Figure 2. The MMDs are plotted for each lunar month. The declinations at the two nearest Moonsets are also plotted. Verticle lines therefore indicate Extrapolation Declination required. [Labels: NORTHERN (+) MAXIMUM MONTHLY DECLINATIONS. SOUTHERN (-) MAXIMUM MONTHLY DECLINATIONS. DATES OF MAXIMUM MONTHLY DECLINATION.]

[*!* Image] Figure 3. The MMDs are plotted for each lunar month. The declinations at the two nearest Moonsets are also plotted. Verticle lines therefore indicate Extrapolation Declination required. [Labels: NORTHERN (+) MAXIMUM MONTHLY DECLINATIONS. SOUTHERN (-) MAXIMUM MONTHLY DECLINATIONS. DATES OF MAXIMUM MONTHLY DECLINATION.]



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