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radius ("semidiameter") s = 15'.5 and a "declination" perturbation amplitude,23 A = 9'.0 (see §2.3.5). The mean declination of all the northernmost moonset azimuth alignment indicators is 29°3'.0, a respectable enough approximation to the extreme northern declination of the Moon. However, Thorn's conclusion of this analysis was that the various alignment indicators were intended to obtain highly precise refinements of the declination, as noted in the last two columns of Table 6.6. For instance, the azimuth alignment over Group Q to the notch was to the Moon's center, with declination 8 = e + i; that of S4 - S5 to the notch indicates an azimuth alignment corresponding to 8 = e + i + s, while the alignment from S1 over the main site to the notch indicates a declination, 8 = e + i - s + A. Thom (1971/1973/1978, p. 48) suggests that the bearing differences of the smaller stones around Si indicate the variation in A, about 1 arc-minute! Unfortunately for Thom's hypothesis that megalithic exploration of the small variables was attempted, the necessary backsights to obtain high-precision alignments for 8 = e + i - s and for 8 = e + i - s - A are not present. Whether the higher precisions implied by the analysis were actually attained or not, the case for intentional alignments to mark the extreme setting points of the major standstill Moon would appear to be strong enough. But there is more evidence yet.

Thom also discovered an alignment to the southernmost setting direction of the Moon from stones S1 and S2 to separate notches in the rolling profile of Ballanoch Hill, 6.3km away at bearings of 203.8° and 207.9°, respectively, which imply a mean declination of -29.1°, but separate declinations 8 = -(e + i + s) = -29.3 and 8 = -(e + i - s) = -28.8°, respectively. The SW alignment from S1 is currently impossible due to groups of trees, but that certainly need not have been the case in the Neolithic.

Thom (1971/1973/1978, pp. 50-51) also suggested that alignments involving stones S3 and S6 could have been used to provide warning of the approach of the Moon to the maximum. If the perturbation in declination (the amplitude or maximum value of which, 9', has been designated A) were to achieve a maximum at the same time that the major standstill did, the lower limb of the Moon (at 8 = 28°29') would have coincided with the notch as seen from S6 one and a half cycles or 260 days prior to the true moment of maximum standstill. If, on the other hand, the minimum were to occur at a major standstill, the lower limb of the Moon would have coincided with the notch as seen from S3 only 1 cycle or 173 days prior to major standstill. Finally, he suggested that the alignment involving the center of Group Q would have achieved the alignment to the Moon at declination 8 = e + i = 29°2'.5, to an uncertainty of 1' only at the epoch b.c. 1700 ± 100, assuming the Moon's inclination to be i = 5°8'43". This is because of the slow variation of e with time (see §4.4).

We are left wondering if high precision at particular sites, using particular combinations of stones and sightlines, was not being achieved afterall. Statistical arguments do not

23 The perturbation is actually on the inclination; at a major/minor standstill, however, the perturbation adds directly to the declination; see Figure 2.17b.

really touch this issue if there is clear evidence of distant enough foresights, or reasonably precise backsights and space for standing platforms at which to record the measurements in some way.

Thom, of course, carried out his own statistical analyses. In one of them (Thom 1971/1973/1978, pp. 75-79), he selected 40 sightlines at 23 sites and from them deduced four values: the obliquity, e = 23°53'26"; the inclination of the Moon's orbit, i = 5°8'52"; the major perturbation of the Moon's inclination (seen in the effect of the declination on the azimuth), A = 9'23"; and a mean semidiameter of the Moon's disk, s = 15'55" (allowing for the upper limb, lower limb, or mid-disk to be the point of alignment on a distant foresight). Of course by preselecting these sightlines as being astronomically relevant, Thom's argument can be construed as circular, but the results are impressive in any case. Now, we will explore possible procedures for observing and recording such observations.

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