Rising and setting positions of the Sun move from south to north and back again along the horizon during the course of a year.
Rate of change is fastest in the middle and slow at the ends. Extreme positions are known as the Solstices and the midpoint is called the Equinox.
Cross-Quarters are halfway in time between an Equinox and a Solstice. These are all marked in amber on the diagram below:
The Moon moves similar distances back and forth along the horizon but does it over the course of a tropical month of 27 / 28 days (27.32 mean).
The most northerly and most southerly moons of the month are called Lunistices in the same way as the extreme solar positions are known as Solstices.
South and north lunistices are about fourteen days apart.
Measuring days of the month along the horizon is not practicable because the moon's positional changes are too rapid & complicated but,
on a longer timescale, lunistice positions are predictable. This is because rotation of the lunar orbit causes the overall extent of the moon's monthly motion along the horizon
to expand and contract with a regular 18.6 year period. Thus the rising/setting positions of the lunistices act as an indirect pointer to the positions of the nodes of the lunar orbit.
The time of minimum azimuth difference between north and south lunistices is known as the Minor Standstill (Min) and
that of maximum range is known as the Major Standstill (Max). These occur about nine years apart.
Blue trajectories in the diagram indicate lunistice positions at 1.16 year intervals. The 18.6 year lunar nodal cycle has been split into 16 equal time periods.
In practical terms the period is 31 Lunistices. A tropical month count alternating between 15 and 16.
This is about 14.3 synodic months and is the closest achievable reconciliation of the lunistice / lunar nodal cycle with the solar year.
Notice how much slower the positional change is at both ends. That is why they are called Standstills.
Also note that minor standstills occur at horizon positions not far from the cross-quarters and that lunar mid-cycle is near to the solstices.
There is clear evidence that the standstill positions of the moon were observed by prehistoric astronomers and
furthermore that the lunistice cycle may have been sub-divided by them into sixteen parts.
Evidence for these calendrical divisions is found primarily in their coincidence with prominent horizon features. It is reinforced by examples of monument axes that indicate them.
Such examples, for each class of division if not each single division, may be found here
and statistical analysis of many prehistoric ritual horizons may be found here.
These divisions and their declinations calculated for c.1800BCE are tabulated below:
- Declination is a measure of the position of an object in the sky, relative to the celestial equator.
- In the notations, '+' / '-' mean: of more / less extreme declination than the named term.
- Given declinations are for the moon's centre, those for the upper or lower limb would be further north or south by approx. 0.26 degree.
- The difference between Declination and Apparent Declination is due to Lunar Horizontal Parallax.
This is the difference between where the moon appears to be and where it actually is.
It varies with observer latitude and altitude of sightline.
- This division of the 18.6 year cycle gives 16 periods (lunar years) of 15 or 16 tropical months.
About one year two months by our reckoning (1.16 year mean).
- The above is a theoretical model generated as a response to certain perceived tendencies in the early survey data.
The match with surveyed prehistoric ritual horizons seems to be good.
However, it has not been proven that our ancient ancestors used a formal, measured system.
The apparent consistency may be a result of rule-of-thumb or intuitive measurements.
It is important to understand that, because the moon has phases, the lunistice cycle must be observed against all four quadrants of the horizon.
There is a natural rhythm to this that would be obvious to any conscientious observer [see "What is a Lunistice"].
The north-west / south-east axis is used from the winter solstice to the summer solstice,
then there is a change-over and the south-west / north-east axis is used from the summer solstice to the winter solstice.
On both axes, priority shifts from the first to the second named direction at the equinox.
The critical moons for observation are the most northerly and southerly ones of the month (the Lunistices) which are about fourteen days apart.
Because the sixteenths are the centres of periods (see Prehistoric Eclipse Prediction), a division of the lunar nodal cycle into thirty two parts is implied,
with the thirthysecondths representing the divisions between the periods.
I resisted dealing with this for a long time because (like the sixteenths before it) I didn't want to accept it and
it could be argued that by creating so many "significant" declinations then one is bound to find something.
However, once again I have done the calculations because of the survey data.
There are various instances of situations where, for example, the major eighth has no accurate marker but
either side of where it ought to be are horizon points equivalent to the thirtysecondths bracketing it.
Obviously, around the standstills it would be difficult enough to distinguish sixteenths never mind thirtysecondths.
This is, I believe, the true reason for Thom's "high precision alignments", his own interpretation being, unfortunately, erroneous and overcomplicated.
Anything that would help improve precision in the period around the standstills would clearly be very useful.
Going further north stretches the declinations over more azimuth.
Arranging for the appropriate rises/sets to occur on a north facing slope does the same thing and there are numerous examples of that in the site catalogue.
Another trick that has become apparent from the surveys is to have the critical declinations occur at a "turning point" such as a step, notch, or rock outcrop,
where small differences would be more noticeable.
Below is the full thirty two part table, good enough for (c.1800BCE) practical purposes: