Discussion of Results


Evidence that the alignments were intended

  • All 13 stones with an indicated lunar band gave a precise alignment for one of the 4 key declinations
  • There are several ‘pairs’ of stones with opposite ‘wobble'

For example         Onich / Achara

Carnasserie / Achnabreac……. and others

  • For 9 of the 13 alignments the foresight is a stone or is rocky (See ‘Conclusions regarding the results found’ below).

In addition the diagrams show that foresights were chosen with care to avoid doubt about the intended foresight.

E.g. Achara (2), Salachary (14), Ford (16), Barnashaig (32)


Chance Alignments

In hilly countrysome chance alignments are to be expected (Heggie 1981: 136-45; Ruggles 1999: 59). Ruggles (1999: 42) illustrates this by analogy to a blind marksman who would sometimes hit a target. What we need is some assessment of the likely occurrence of chance alignments. This was done by examining a total of some 1500 degrees of random hilly horizon in the surveyed region from identifiable backsight positions. This contained 30 lunar bands and so potentially 30 alignments.

Three chance alignments were found.

Therefore in this study 1 in 10 random Lunar Bands contained an alignment.

Since the 13 sites are independent of each other, the probability of them all being chance is vanishingly small. (0.1^13). There is no reason to suppose that the sample used was abnormal


 Conclusions regarding the results found

The following has been found:-

a)    The 13 sites that could be fully assessed all gave a precise lunar alignment in the indicated lunar band.

b)    The declinations found were all within 2ʹ arc of a key declination

c)    There is internal consistency in the results found (see ‘Evidence that the alignments were intended’ above).

When the results of the Chance Alignment investigation are included the evidence tells us that the alignments are real and were planned.

The criteria for this study were heavily dependent on the criticism by Ruggles and Heggie of Thom’s investigations, because they effectively specified what was required to resolve any debate.

The result of all acceptable backsights having precise alignments is remarkable and, given that chance alignments were not very common, fully justifies the claim that precise lunar alignments in this region were deliberately set up. No opinion is involved.  The measurements are empirical and the calculations are routine, if laborious. The stones are there for anyone to measure.

The  existence of precise lunar alignments and the arguments that such alignments could not be set up are mutually exclusive.  The results of this study mean that issues surrounding refraction, parallax, extrapolation, weather etc. need to be revisited to answer the question, “How were the alignments set up?”

What follows below should be the beginning of a new area of thought. I have no expectation that this will be the final word, and indeed hope that it is only the beginning of a productive debate. Previous issues on the feasibility of establishing precise alignments are discussed. Ways in which the difficulties may have been overstated, and ways in which they could have been worked around are suggested.



Astronomical refraction is a known issue. It is accepted that refraction at very low altitude may vary considerably from the standard value. A study by Schaefer and Liller (1990) for the setting sun found widely varying refraction values with a rms deviation of 0º.16 and a probable range of 0º.64. In the same paper there is mention of a brief study by Seidelmann for altitudes in the range 0º.2 to 3º.0 where the rms deviation of three sets of measurements was 3ʹ.0. The authors conclude that:-

"The historically important claim by A. Thom that the British megalithic sites were used as accurate observatories is shown to be wrong because the needed accuracy is much greater than can be obtained for long averaging intervals."

However the study by Schaefer and Liller was for an altitude of 0º using observations of the sun setting over the sea. The large deviations found are of particular significance in precise archaeoastronomy only when altitude measurements are made below 0º.5. The range of altitude in precise archaeoastronomy is usually 1º to 5º.

To add to the available information, I made three sets of timed measurements of the altitude of the setting sun (both limbs) to as low an altitude as possible; to below 1º where the horizon permitted. The altitude from these measurements was calculated (Hc) and compared with that observed (Ho), the difference giving the deviation.

Two different locations were used (one inland site (two sets), one near the sea). The total range of altitude was from 0º.24 to 4º.0. There were 57 observations and the mean deviation was ǀ0ʹ.6ǀ.


Range of Altitude  Number of  observations Range of Deviation     Mean Deviation
  0º.24 to 0º.5  7 observations  + 0′.1 to  − 3′.0      |1ʹ.7|
  0º.5 to 1º.0 11 observations  + 0′.4 to  − 2′.5      |0ʹ.8|
  1º.0 to 4º.0, 39 observations  + 0′.8 to  − 0′.4      |0ʹ.29|


These values are much smaller than those found by Schaefer and Liller which is to be expected because of the difference in altitude, but they are also much smaller than those found by Seidelmann whose observations were for a similar altitude range. Reijs (2001) gives a graph of altitude vs refraction combining the results of Schaefer et al., Seidelmann and others which suggests that serious refraction problems are mainly to be expected at altitudes below about 0º.3. The results given above suggest that at altitudes above 1º.0 there is not a serious problem and that even down to 0º.5 difficulties may be manageable. In this study one site had a very low altitude: Lower Fernoch (34) (0º.19). The lowest of the remaining twelve was 1º.70.

Terrestrial refraction also occurs but the evidence shows that this does not seem to be an issue:-

1)    Most of the sites in Argyll have had multiple visits. The declination values found rarely varied by more than 0ʹ.5 arc.

2)    In his reassessment Clive Ruggles reported:- Resurveys of 38 of the 44 sightlines produced general agreement with the Thoms’ declinations to within about 1ʹ (Ruggles 1983: S32).



Changes in lunar parallax (54ʹ to 60ʹ arc) would be expected to make it very difficult to set up an alignment to the precision found. The assumption by Thom which others accepted was that it would be necessary to average results over 100 years or more (Thom 1971: 81-82; Heggie 1981: 178; Ruggles 1999: 66).

The following might offer a partial solution:-

Declination transfer by use of the stars does not seem to have been previously considered. This could be achieved as follows:- From the observing position of a known alignment, observe by how much any suitable star8 ‘misses’ the foresight (a finger width at arm’s length? or more precisely with a simple tool) – amount X. Having previously found a potentially suitable new horizon feature at a different site, use amount X from the same star to find the backsight position. (Change of latitude has only a small effect). This could be checked on any clear night when the star is suitably placed. Fine tune at the next standstill. During the eighteen years between standstills a small group of skilled observers could set up many precise alignments by, in effect, copying the declination of a known alignment to a new site.  The value of the lunar parallax during the prehistoric standstills is known and it was sometimes close to the mean value.  If the method described above was used then it is possible that by chance it was done during a period when the lunar parallax was close to the mean value which would help to explain the high precision achieved. i.e. About any of 1760BC, 1670BC, 1570BC (Thom 1971: 82). (This would not resolve how the original sites were established.)

It is also possible that changes in parallax were known and allowed for.



To determine the extreme value at any given lunar maximum, extrapolation would presumably be required but the evidence to date is very limited. Thom gives the theory of a method (Thom 1971: 83-90) and Wood explains how it could be done with a rope and pegs (Wood 1978: 114-139). The enigmatic stone rows in northern Scotland may have been used for extrapolation purposes (Myatt 1988; Thom 1971: 91-105).

Before any extrapolation method could be devised, it had to be recognised that it was necessary. This could have arisen from careful observation of the setting position of the moon at the major standstill - perhaps casual at first but later using posts. In the north for example it would have been noticed that the moon did not come smoothly to its maximum position but for about a year was always in the same region9. Further observations could eventually lead to the knowledge that the position of the moon on the horizon during a lunation maximum was generally erratic, occasionally reaching what seemed to be a maximum position. Hence to the need for extrapolation. ‘…it is possible to develop a detailed knowledge of astronomy using the simplest of technology.’ (Parker Pearson 2005: 128)

The evidence that extrapolation in some way was done lies in the results found in this study as stated in ‘Conclusions regarding the alignments found’ above.

Then we have:-

a)     The alignments were intentionally set up

b)    This could only be achieved by determining in some way the maximum lunar position to high precision.

c)    Except by chance the moon does not rise/set at the extreme north/south

d)   To determine the maximum position three or more observations near the maximum must be made and the actual maximum found from these observations.

The small rms residuals for the declination values found means that some method for determining the extreme position of the moon from the observations made was used.  We therefore reach the conclusion that either extrapolation in some way was done to enable the sites to be set up or they were set up using some unknown method.



Dating of the sites

Occasionally when a standing stone has fallen, material is found which can be carbon dated. Up to the present such material has only been found at sites which are not lunar but are possibly calendrical (sun) (Mackie 1973; Martlew and Ruggles 1993). If a single stone has fallen, and probably therefore gives no indicated direction, we cannot determine whether or not it had been lunar. Therefore we have been unable to determine if any dateable material found is associated with a lunar site. However the present study potentially changes this for if the fallen stone is one of a pair or a short row and the site found to be lunar then any dateable material found might indicate the construction date.

(There are other alignments determined as lunar which have features which warrant archaeological investigation. E.g. Barnashaig (32) and ‘Lower Fernoch’(34) both in Argyll).

At present we are left with deriving a date from the declinations as given in 2. ‘Declination Values Found’ under Discussion, Analysis of results.  The rms of the difference between the observed and the theoretical values is only about 1ʹ of arc which tells us that the theoretical values are essentially correct. (If they were not then we would not find such close agreement.) Those theoretical values depend upon the value of the obliquity of the ecliptic (ε) which Thom determination as23⁰ 54ʹ.2 ± 0ʹ.7 (Thom 1971: 36-44).    Since this value of ε (which decreases by about 0ʹ.7 per century) is central to the determination of the standstill declinations ( ± 29⁰ 03ʹ and ± 18⁰ 45ʹ.6)  it follows that the value of ε derived by Thom must be correct to within about 1ʹ of arc. This would be the value in about 1700 BC. There has long been controversy about the validity of the solstial sites used by Thom, especially Kintraw, but the above independent determination of the value of ε provides support for the correctness of Thom’s solstitial sites from which he obtained the value


 Other considerations

Weather preventing observation   There is evidence that the climate in northern latitudes was nearly ‘Mediterranean’ in the EBA with clearer skies. (Wood 1978: 182-184)

Vegetation at foresights 

a) Pollen analysis suggests that there was less tree cover than now (Wood 1978: 182-184).

b) Grass and bushes would have been likely to be present. The fact that in this study 9 of the 13 sites had rocky foresights may be relevant to this.

Changes in ground height/ movement of stones  The results found imply that any changes in ground height are not sufficient to significantly affect the alignments. A stone that is no longer upright, or a row with fallen stones, may still fulfil the backsight criteria by giving an acceptable indicated direction, depending how it is leaning, or has fallen and/or what usable skylines are visible. Applies at Salachary (14), Achnabreac (29), Barnashaig (32) and Lower Fernoch (34). There is precedent for this (Ruggles 1993; 1999: 113-14).


There are a number of Related Topics for Discussion available here .

These include:

Sun/Moon knowledge in the Late Neolithic

Evidence for a Hierarchical Society     and

Discussion on Ritual, Culture and the Results Found




If it was possible to observe the moon on the horizon in daylight this would be of considerable assistance.  The following section discusses this.

  • There follows discussion of five sites all for either   + s + Δ  or  - s + Δ  in the north

i.e. for the maximum north that the upper or lower limb could ever have reached.   This in itself is important – the moon could never have reached further north – but there could be further point.

The sites have all been discussed individually previously.  They are:-

Group 1 For the rising moon:- #16 Ford and  #32 Barnashaig.

Viewed on the same days in September in darkness with successive observations about 24 hours apart.   (See diagram after Morrison in Analysis above, or Thom & Thom MRBB 1978, p11)

Group 2 For the setting moon:-#20Nether Largie, #21Ballymeanach, #24Torbhlaran

Viewed on the same days in March in darkness with successive observations about 24 hours apart.  (Same references as above.  Morrison; Thom & Thom )

At each site observations would be made over, usually, 3 successive nights with observations about 24 hrs apart and extrapolation (see later) used in order to find the extreme position.  Only by chance will the moon be observed on the horizon at or very close to its extreme north/south for that lunation.  However on about 50% of occasions will be within 3ʹ arc of the lunation maximum and rarely as much as 10ʹ arc from it .   In 12 hrs the change would be only ¼ of that amount.   Extrapolation would still be required but the finer detail would have been very useful.   In order to achieve this, observations at one of the sites would have to done in daylight (in which case the moon would be at the ‘other’ quarter from that shown above).  e.g In September a 3rd quarter  moon rising at Ford in the night would be setting 12 hrs later in daylight at Nether Largie.  Given the unpolluted skies at the time perhaps observations in daylight could have been done.

(Daylight observations would very probably have been possible at Carnasserie and Salachary     (-29º 27’.5 ) with the moon low in the south; especially at the former where the low sun would have been setting behind a nearby hill.)