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S1, S3, & SX to Drygarnfawr Cairns

S1 and S3 Llananno to DrygarnFawr alignments extrapolated to lunar standstill limiting positions.

From the two photographically established backsights S1 and S3 we may extrapolate to the approximate positions of further pertinent stances which might have been employed in the complex calculatory procedures necessary to find the true position and timing of a Southern Major Lunar Standstill

All alignments shown are for the upper limb of the Moon when the dead centre of the lunar disc has the declinations given.

The lunar alignments to Drygarnfawr cairns struck from S1 and S3, when established reliably, may support calculated extrapolation to find the position of further backsights employed at lunar standstill observations.

S1 to Drygarnfawr East Cairn declination deficiency.

s1 llananno to Drygarnfawr East cairn has been established as having a declination deficiency from the Southern Major lunar standstill of exactly two apparent mean diameters of the Moon = (e+i)-2D = 28 01'.
See S1 Drygarnfawr.
Markers for this deficiency position have been found at other lunar standstill sites. See S1 Llananno to Y Glog, Montgomeryshire. These may be early warning markers as this stance would bring the Moon down on the East Cairn horizon marker some 30 hours before the standstill proper.
Alternatively these may be anchor positions for the calculations necessary to locate the peak of the standstill parabola.

The declination values of the two sagittae 4G employed in geometric methods of extrapolation as calculated by Alexander Thom

S3 Llananno to Drygarnfawr East Cairn declination deficiency.

S3 Llananno to Drygarnfawr East cairn has been established as having a declination deficiency from the lunar standstill very near the 4g position as imputed by Alexander Thom for the sagitta of the parabolic curve of the path of the Moon at a Major Standstill.
(e+i)- K (4G).
See S3 Drygarnfawr.

The alignment to Drygarn East Cairn from the stance for the positive extreme declination of Cyclic perturbation at a Souther lunar standstill runs very close to two major cairns

Stances for Cyclic Perturbation

To either side of the stance for the standstill proper, (e+i), there may be marks for the extremes of Cyclic Perturbation (p). Thom had found that most of the later established lunar standstill sites catered to the perturbation positive extreme. Here we see how close to two major cairns this alignment lies,- Pegwyn Mawr and Pegwyn Bach, - (e+i)+p