Glossary X
At a lunar backsight where permanent or temporary ancillary extrapolation gear has been set up there should be a length preserved between major stones which is the 4G for this site. This 4G represents, on the ground, the lateral distance an observer must move in order to 'shift' the Moon through the declination range K. K is the change in the Moon´s position during the 24 hours preceding a standstill. At a Major Standstill it is 46.5 arc minutes and at a Minor Standstill 30 arc minutes. See also- K, ANGULAR DISPLACEMENT, EXTRAPOLATION PROCEDURE, LUNAR STANDSTILL.

S2 Llananno to y Glog tumuli group.

Northern Major lunar standstill alignments from S2 Llananno rock- cut throne to y Glog hill tumuli, Dolfor, Montgomeryshire, Powys.

The Glog Hill earthen barrow group is one of the largest Bronze Age cemeteries in the United Kingdom. Ten tumuli ascribed to the Middle Bronze Age period have been identified on the crest of this prominent 1500ft, 480m hill.
Of the ten tumuli the 6/7 at the western end of y Glog offer lunar extreme declinations as viewed from stone chair S2.

These six western most tumuli on y Glog straddle the lunar disc when rising at a Northern Major Standstill.

The foresights-

The pertinent tumuli from S2, Llananno.

At a Northern Major Standstill moonrise circa 1800 BC the full disc of the Moon plus the full amplitude of Cyclic Perturbation positive and negative, fell across these six tumuli to the western end of y Glog hill. The observing stance is from S2, Llananno stone chair on Brondre Fawr ridge.

The backsight- S2, Llananno stone throne.

The seat faces north east. This 2 to 3 tonne block is marked as a parish boundary stone on OS maps. It is not yet a recognised and conserved antiquity.
When sitting comfortably in this chair the eye is directed to y Glog.

Rock- cut chairs.

There are two large blocks carved to seat forms on Brondre Fawr ridge, S1 and S2, Llananno, 223.5 metres apart. The larger, S2, to the south, weighs in excess of 2.5 tonnes and stands 1.5 metres above ground. This stone is carved with a ledge on the north eastern side such that an observer sitting here has their attention directed to y Glog hill.
There are at least ten tumuli still identifiable on the crest of y Glog.

Long- exposure photography of rising or setting Moon.

Reliably accurate positioning of the lunar disc as it crosses the horizon may be ascertained by long exposure film photography. With multiple shooting on the same alignment in the years surrounding a lunar extreme digital surveys may be supported which establish high resolution declinations of points on the horizon.
Using 35 mm slr film equipment secured to heavy tripods, with 185 to 200 mm lenses and remote shutter locks, these long exposure shoots may run for 30 to 60 minutes

Accurate layering or montage of multiple long-exposure photographs.

Close estimation of the declinations of the tumuli on y Glog may be derived from high resolution photography. Many photographs of moonrises on this hill have been secured in the years surrounding both the major standstills of 1987 and 2006.
Here we have three long exposure photographs of the Moon setting on Glog Hill taken at different dates from the same position- the stone throne S2, Llananno. The three images are accompanied by lunar data for these times read from NASA/US Naval Office Data Services.
Layered presentation of several sets of long exposure 35mm film images on the alignment S2 Llananno to y Glog Hill tumuli cemetery. The data for three of the most reliable images is shown.
The declinations of all horizon points along the hill may be extrapolated digitally from each of the photographs independently. When all extrapolations agree to a resolution of better than one arc minute of declination then we can be assured that the astronomical tumuli positions have been verified reliably.
The distance to y Glog is 5.5 miles, (8.8 km).
There are at least ten tumuli still identifiable on the crest of y Glog.

The case for the Northern Major Standstill with positive Cyclic perturbation in 1800 BC, (e+i+p).

When the astronomical positions of the horizon features have been reliably established we may extrapolate lunar standstill positions to past years and alternate perturbation conditions.
An extrapolated track for any local position may be created to show the situation on a target date past or future.
Looking northerly in these latitudes the lunar declination tracks are becoming circumpolar and curve increasingly near the horizon. Here is the lunar path for the Northern Major Standstill with maximum Cyclic perturbation @ 1800 BC, (e+i+p),- corrected for mean lunar diameter.
From this extrapolation we see how the ancient astronomers capitalised on this fortuitously angled western hill flank of y Glog. This slope averages the curving path of the moonrise at this northerly direction allowing a mobile observer much extra time to adjust the spark of the lunar upper limb in the notches between tumuli and mark accurate stake settings.

(e+i+p) @ 1800 BC.

The maximum northern position that the Moon can reach in it's orbit is an aggregate of three terms,
e = Angle of obliquity to the Ecliptic, = 23° 53' (Tilt of the Earth's equator relevant to it's orbital plane @ 1800 BC.)
i = Inclination of the lunar orbit = 5° 8.7' (Angle of the Moon's orbit to the Ecliptic)
p = Cyclic perturbation = + & -9' (Orbital wobble with an amplitude of @ 7 months)

At the time of Thom's publication Megalithic Lunar Observatories obliquity, was estimated to have diminished by 27' in 4000 years, - 40.5 arc seconds per century.

Inclination, i, is thought to have been relevantly stable for thousands of years.

Perturbation p, is also estimated to have remained steady for millenia.

Digital extrapolation to moonrise at a Northern Major Standstill circa 1800 BC.

With these optimum conditions the upper limb of the Moon will glide from one notch to the next giving a great extension to the time for observations. On a flat horizon the Moon will rise in less than four minutes. Along a hill slope as we have here the disc may take 10 minutes or more to clear the horizon.

The limiting positions of Cyclic Perturbation

There may be three limiting positions observed at a standstill- positive, mean and negative Cyclic Perturbation it is only at the standstill periods that the current perturbation status might be observed and assessed. It is vital that the perturbation condition is monitored over the standstill period and isolated from the movements of the standstill proper.
Thom noted that the later observatories appeared to favour alignments to maximal perturbation ...(e+i+p) as above...
Whilst earlier lunar observatories catered for foresights aligning to the minimal, mean state of perturbation ..(e+i) as follows.

Northern Major Standstill with mean Cyclic perturbation in 1800 BC, (e+i)

Northern Major Standstill at mean Cyclic Perturbation
The tumulus at e indicates the first flash of the upper limb of the Moon at this condition of perturbation There are no markers for the lower limb.

Northern Major Standstill with negative Cyclic perturbation in 1800 BC, (e+i-p).

Northern Major Standstill at negative Cyclic Perturbation- (e+i-p). Both upper and lower limbs of the lunar disc with negative perturbation are indicated here by tumuli f and h.

Digital surveys of high resolution photography.

With the approach of digital surveys performed on good resolution photography we may circumvent several basic parameters of traditional spherical astronomical calculations. Taking the apparent diameter of the heavenly body at the moment of the photography- from USNO data- we have a precise scale with which to measure, horizontally, the arc angle of the entire horizon in a photograph. Using this system we need neither the azimuth of the points under scrutiny nor the elevation nor estimation of atmospheric refraction. Also, if any extreme cloud or terrestrial refraction effects are concurrent with the photographs they will be observable and directly measurable. In effect, if the photographs are taken at, or near, the dates which the alignment caters to, we are simulating the observing practices of the ancient astronomers at the correct times of day/ night and, for the Sun, in the same season, as the original establishment of the alignment