Periods
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This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th April 1994 but remained unpublished. For readers of the Matrix of Creation (2nd ed, Inner Traditions Press, 2004) it marks the discovery of a unit of time proposed and named the Chronon, as being 1/10000th of the Moon's orbit and also the difference between the sidereal and tropical day of the Earth. The paper also documents a discovery made, with Robin Heath, later to be documented in his books: that one can divide up the solar year by its excess over the eclipse year to reveal an 18.618:19.618 ratio between these years, and many other interesting numerical facts not mentioned in this place. The puzzle here is a connection between the rotation of the Earth, the solar year and the precession of the Moon's orbit which (a) may be explainable by science (b) appears to have puzzled Megalithic astronomers and (c) should puzzle us today.
by Richard Heath and Robin Heath
We find that the Earth’s rotational day divides the year according to the 18.62 year cycle of the Lunar Nodes. From this we conclude that the Earth’s orbit, the Moon’s orbital precession and the Earth’s rotational velocity are most probably interconnected. The tropical solar year in days is factorised almost exactly by 18.618 times 19.618 and the Moon travels one ten thousandth of its orbit in the time difference between sidereal and tropical days.
We have been considering a range of numerical coincidences present in arithmetical and geometrical analyses of astronomical cycles involving the SunMoonEarth system. There is an apparently lawful relationship concerning the Earth, Sun and Moon, one that is most unusual.
The Earth ‘s rate of rotation is directly proportional to the ratio of angular velocities of the Sun and the Moon ~ orbital nodes; as seen from Earth.
The reason why this fact has been hidden is that we use the day or the degree to manipulate the data concerning these phenomena and since the day is implicated in the above law it obscures the relationship and the degree changes the numbers to further obscure it.
We now refer to the angle traveled by the sun on the ecliptic in one day as a DAY. If we convert the Moon’s average daily motion of 13.176 degrees per day to DAYs per day we obtain 13.368 DAYS per day. This is the sidereal frequency per year because DAYS per day is also revolutions per year. This shows the virtue of using DAYS over degrees.
As there is not a great deal of familiarity with the terms used in describing Sun and Moon phenomena, we will recap some terms (see Figure 1).
 The Moon crosses the Sun‘s path or ecliptic at two places, the lunar nodes.
 Full or new moons occuring near a node produce solar or lunar eclipse respectively.
 Whilst the Sun moves East day by day by about one degree, it precesses the Lunar Nodes in the opposite sense, i.e. retrograde. The Sun moves about 18.618 times faster than the precessing nodes.
 Whilst the Sun returns to the same place on the ecliptic after one Solar Year, it will return to a given node after a shorter period an Eclipse Year. In Earth days, a Solar Year is 365.242 units long whilst an Eclipse year is 346.620 units long.
The ratio of 1:18.618 between the angular velocity of the Sun and the Nodes means that after 18.618 solar years, the Nodes will return to the same part of the sky, a period called the Draconic Period. This means that after 1 solar year, the nodes have traveled by 1 /18.618 of the ecliptic. During 18.618 solar years there are 18.618 + 1 eclipse years, the + 1 being due to the complete revolution of the nodes in that period. Because there are 19.618 eclipse years in a Draconic Period, then the nodes must move by 1 /19.618 of the ecliptic in an eclipse year, i.e. before the Sun again meets a given Node. When we draw the ecliptic geocentrically as a circle and place a SunNode conjunction at the "top", then the eclipse and solar year node movements can be shown as in Figure 2.
The question then arises: What is the proportion of the whole circle, shown δ, between the end of the eclipse year and the end of the solar year? It is,
1 /18.618  1 /19.618  which is  19.618 18.618 18.618 x 19.618 
or  1 /365.248  of a solar year! 
In other words, the Nodes move in the excess of the solar year over eclipse year by the equivalent of one Earth DAY on the ecliptic. There are 365.2421 tropical days in a solar year. Thus we can state,
The solar year, in days, has the two factors 19.618 and 18.618 and both these numbers are generated by the Moon 's nodal motion with respect to the Sun.
The Earth’s rotation is the lowest common denominator in the numerosity generated and thus calibrates the cycles involved.
Because of the 18.618 ratio between Sun and Nodal motion, there must be 18.618 days difference between the eclipse and solar years. What also has to be true is that the eclipse year is (1 8.618)2 days long or 346.63 days, which is close to the 346.62 days given [Astrophysical Quantities, C.W. Allen, 1973]. We have come to refer to 18.618 days as a NODE DAY, the time it takes the nodes to move by one DAY on the ecliptic and a fundamental constant in SunEarthMoon astronomy.
We therefore reassert that,
The Earth ‘s rate of rotation is directly proportional to the ratio of angular velocities of the Sun and the Moon ‘s orbital nodes; as seen from Earth.
because,
The Earth rotates once, with respect to the Sun, in the time it takes the Sun, seen from Earth, to move by the amount the Lunar Nodes move in the excess of the solar year over the ed ipse year.
We found another calibrating factor when we moved to DAYs instead of degrees. When we divided 13.176 degrees per day by 360 degrees, we obtained the fraction of a lunar orbit per tropical day. The value is 0.0366009. The same calculation for the sidereal day yields 0.0365009, and both happen to be the number of days in a year of the other type of day, in 1 /10000 ths of a complete lunar orbit. The sidereal day is 365 ths and the tropical day is 366 1 /10000ths of a lunar orbit: the difference between the two is a calibration unit of 1 /10000th.
Therefore, we found that,
The Moon moves 1/10000th of its orbit in the time between one sidereal day and one tropical day. There are 365 such periods in a sidereal day and 366 in a tropical day.
The present understanding of the EarthMoon system does not account for either of the above calibration effects.
© 1994 Richard D Heath, all rights reserved
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The Metonic Period is the 19 year anniversary of the Moon which dominates the repetition of cyclic astronomical aspects in the sky. We know that the megalithic identified this period and others of similar length (the Saros and Nodal periods), because interrelated units of measure, especially the megalithic yard and royal cubit, can be found within monuments which recorded these periods as counted lengths.
How the Metonic Works
There is only numerical way to arrive at a system in which there is an anniversary between the sun, the moon and the stars over 19 years (as in the Metonic period), involving having a lunar orbital period (around the earth) which divides into the same period, in this case exactly 254 times.

 254 lunar orbits of (on average) 27.32166 days equals 6939.7 days
 19 solar years of 365.2422 days equals 6939.6 days and
 235 lunar months of 29.53059 days equals 6939.7 days
If the moon returns to the position of the sun after 19 years then the phase of the moon will be the same so that there will be 254 minus 19 equal to 235 lunar months in the Metonic observatory and it is in the nature of orbits which become commensurate with each other (as discrete, wholenumber gravitational systems), to fall into such resonant relationships rather than chaotic ones.
Signature Ratios within the Metonic
Since the solar year, lunar orbit and month are synchronous, the excess of the solar over lunar year will form a near rational (i.e. integer) fraction of months or orbits, in that case an excess of 7/19 (0.368) lunar months.

 The lunar orbit is 27.32166 days
 The lunar month is 29.53059 days
Similarly, the excess of the lunar month over the lunar orbit become the rational and fractional ratio found between their frequencies within the 19 year Saros cycle, that is 254/235; which has the fractional part, reciprocated of 1/0.08085 = 12.368 which is then N for the N:N+1 triangle describing the orbit relative to the month, of the moon.
However, the lunar orbit is also found to be 10,000 time periods long, the unit of time being the excess of the solar over the sidereal day***, which in Matrix of Creation I called the chronon after the god of time.

 *** The sidereal day is relative to the stars and it is the time for the earth to rotate once whilst the solar day is that time plus the time taken for a location upon the earth to catch up with the sun's motion within the solar year, this due to the earth's orbit around the sun.
Once the earth's rotation and lunar orbit came to be set to this chronon ratio of one solar excess to ten thousand solar excesses per orbit, the orbit of the moon can be visualised as containing 10,000 chrononinches as a length (the circumference of the Le Menec western cromlech near Carnac town in Brittany) and this actual length of 10,000 inches can be divided by the number of orbits in the Metonic so as to create the 39.37 inch metre standard (its legal ratio in the U.S.A [Berriman 1953, p21]) which is 10,000/254 inches.

 We will later look at how three quarters of this length of 39.37 inches equals 29.528 inches, one part in 9742 of the lunar month's average duration of 29.53059 days, a relationship seen very clearly at Le Manio's Quadrilateral [HEATH & HEATH, 2010 & HEATH 2014] marking a count of three solar years and three lunar years, and their difference of one megalithic yard of 261/8 dayinches.
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The stone age person had significant contact with the natural world and, with this, the sky. By night many bright points appear upon the black dome of the celestial sphere at night, as a fixed pattern, and the moon is then like a weaker version of the sun. Day begins when the sun appears on the eastern horizon (to define morning) and sets in the west (to define evening). It would therefore soon become clear, to stone age observers, that the starry points we now call stars move like the sun by rising in the east and setting in the west.
A sixfold hexad of three dimensions as they affected megalithic astronomers
Hyparxis (In Greek, ὕπαρξις) means 'essential nature' and is the Neoplatonic term for the summit, beginning, or hierarch of a hierarchy, as follows: The word is particularly used by the Neoplatonist, Proclus who uses it to mean "the summit of any nature, or blossom, as it were, of its essence."
Eternity is cyclic and often symbolized by the image of a snake swallowing its own tail, known as the Ouroboros (or Uroboros). The circle is also commonly used as a symbol for eternity, as is the mathematical symbol of infinity, .
Time is the fourth dimension and a measure in which events can be ordered from the past through the present into the future,^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]} and also the measure of durations of events and the intervals between them.
This recurrence, of celestial luminaries rising in the east and setting in the west, is generated by the rotation of the earth and, in the late stone age, marked bones and other objects indicate that longer time periods such as the lunar month were being counted for many thousands of years, as one mark per day.
The lunar month was therefore the original example of cyclicity, through which the stone age could usefully count days so as to somewhat predict the future appearance and disappearance of the moon at night, and quite possibly discover connections between the tides, and other cycles relating to the moon.
The arrival of the sun on the eastern horizon is however not constant as the sun moves towards the north in summer and towards the south in winter, leading to the variations in climate throughout the solar year of 365 days, a cyclicity best identified in the movement of the horizon events (sunrise and sunset) of the sun. The moon also rises further north and south but over a shorter period, this corresponding to the moon's orbit of the earth every 27 1/3 days.
The megalithic clearly studied these variations (of the alignment of horizon events, of sun and moon) within suitably large monuments, these therefore commemorating, through definite alignments to the horizon,the cyclic journey of the solar year and lunar orbital variations, whilst also preserving (for us) the astronomical practices of the megalithic.
The cosmic cycles seen from earth are called synodic periods because they only exist when the observer's motion (due to a moving and rotating earth) are factored in. Synodic periods could be counted in days by the megalithic astronomers and (when each day was given a unit of constant length) a geometrical line resulted. Such counted lines physically represented the duration of a given synodic period, against which other (synodic counted) lengths (representing other cosmic cycles) were compared, within the geometric form of a right triangle.
Synodic periods would then have been found to hold significant numerical ratios between each other and these invariant ratios can be seen to follow simple geometrical or harmonic rules, some of which can be recognised within the design of megalithic monuments. One example of a geometrical synodic ratio is that the length of the solar year relative to the lunar year is identical to the length of the diagonal of a four squares rectangle relative to its four unit long side. An example of musical harmonic ratio is the length of the Jupiter synod relative to the lunar year is the whole tone ratio of 9/8.
Geometrical invariants based upon synodic counted lengths are certainly visible in megalithic monuments, alongside the alignments to the horizon. There is also evidence of alignments pointing to the northern horizon, where the only objects to align to were the circumpolar stars which display directly the rotation of the earth and the recurrence of the day due to that rotation causing sunrise in the east and sunset in the west and the movement of the celestial sphere.