Geometry 6: the Geometrical AMY

By 2016 it was already obvious that the lunar month (in days) and the PMY, AMY and yard (in inches) had peculiar relationships involving the ratio 32/29, shown above. This can now be explained as a manifestation of day-inch counting and the unusual numerical properties of the solar and lunar year, when seen using day-inch counting.

It is hard to imagine that the English foot arose from any other process than day-inch counting; to resolve the excess of the solar year over the lunar year, in three years – the near-anniversary of sun and moon. This created the Proto Megalithic Yard (PMY) of 32.625 day-inches as the difference.

Figure 1 The three solar year count’s geometrical demonstration of the excess in length of 3 solar years over 3 lunar years as the 32.625 day-inch PMY.

A strange property of N:N+1 right triangles can then transform this PMY into the English foot, when counting over a single lunar and solar year using the PMY to count months.

The metrological explanation

If one divides the three-year excess (here, the PMY) into the base then N, the normalized base of the N:N+1 triangle. In the case of the sun and moon, N is very nearly 32.625, so that the lunar to solar years are closely in the ratio 32.625:33.625. Because of this, if one counts 

  • months instead of days,
  • using the three-year excess (i.e. the PMY) to stand for the lunar month,
  • over a single year,

the excess becomes, quite unexpectedly, the reciprocal of the PMY;

One has effectively normalized the solar year as 12.368 PMYs long. This single year difference, of 0.368 lunar months cancels with the PMY; the 0.36827 lunar months becoming 12.0147 inches. Were the true Astronomical Megalithic Yard (AMY of 32.585 inches) used, instead of the PMY, the foot of 12 inches would result. Indeed, this is the AMYs definition, as being the N (normalizing value) of 32.585 inches long, unique to the sun-moon cycle. The AMY only becomes clear, in feet, after completion of 19 solar years. This Metonic anniversary of sun and moon over 235 lunar months, is exactly 7 lunar months larger than 19 lunar years (228 months).

But this is all seen using the arithmetical methods of ancient metrology, which did not exist in the megalithic circa 4000BC. Our numeracy can divide the 1063.1 day-inches by 32.625 day-inches, to reveal the AMY as 32.585 inches long, but the megalithic could not. Any attempt to resolve the AMY in the megalithic, using a day-inch technology***, without arithmetical processes, could not resolve the AMY over 3 years as it is a mere 40 thousandths of an inch smaller than the PMY. So arithmetic provides us with an explanation, but prevents us from explaining how the megalithic came to have a value for the AMY; only visible over long itineraries requiring awkward processes to divide using factorization. However, by exploiting the coincidences of number built in to the lunar and solar years, geometry could oblige. 

***One can safely assume the early megalithic resolved
eighths or tenths of an inch when counting day-inches.

The geometrical explanation

In proposing the AMY was properly quantified, in the similarly early megalithic cultures of Carnac in France and the Preselis in Wales, one must turn to a geometrical method

  1. One clue is that the yard of 3 feet (36 inches) is exactly 32/29ths of the PMY. This shows itself in the fact that 32 PMYs equal 29 yards.
  2. Another clue is that the lunar month had been quantified (at Le Manio) by finding 32 months equalled 945 day-inches. By inference, the lunar month is therefore 945 day-inches divided by 32 or 945/32 (29.53125) day-inches – very close to our present knowledge of 29.53059 days.

From point 1, one can geometrically express any length that is 32 relative to another of 29, using the right triangle (29,32). And from point 2, since the 945 day period is 32 lunar months, as a length it will be in the ratio 29 to 32 to a length 32 PMYs long, the triangle’s hypotenuse.

Point 1 also means that 32 PMY (of 32.625 inches) will equal 1044 inches, which must also be 29 x 36 inches, and 29 yards hence handily divides the 32 side of the {29 32} right triangle into 29 portions equal to a yard on that side. One can then “mirror the right triangle about its 29-side so as to be able to draw 29 parallel lines between the two, mirrored, 32-sides, as shown in figure 1. The 945 day-inch 29-side which already equals 32 lunar months (in day-inches), now has 29 megalithic yards in that length, which are then an AMY of 945/29 day-inches!

Figure The 29:32 relationship of the PMY to the yard as 32 PMY = 29 yards whilst 32 lunar months (945 days) is 29 AMY.

Comparing the two AMYs and their necessary origins

Using a modern calculator, 945 divided by the PMY actually gives 28.9655 PMY and not 29, so that 945 inches requires a unit slightly smaller than the PMY and 945/29 gives the result as 32.586 inches, which length one could call the geometrical AMY. This AMY is 30625/30624 of the AMY in ancient metrology which is arrived at as 2.7 feet times 176/175 equal to 32.585142857 inches. By implication therefore, the ancient AMY is the root Drusian step whose formula is 19.008/7 feet whilst the first AMY was resolved by the megalithic to be 945/29 inches.

This geometrical AMY (gAMY?) obviously hailed from the world of day-inch counting, which proceeded the ancient arithmetical metrology which was based upon fractions of the English foot. The gAMY is 32/29 of the lunar month of 29.53125 (945/32) day-inches, since 945/32 inches × 32/29 is 945/29 inches.

Using ancient metrology to interpret the earliest megalithic monuments may be questionable in the absence of a highly civilised source which had, in an even greater antiquity, provided it; from an “Atlantis”. In contrast, the monumental record of the megalithic suggests that geometrical methods were in active development and involved less sophisticated metrology, on a step-by-step basis.  From this arose the English foot which, being twelve times larger than the inch, could provide the more versatile metrology of fractional feet, to provide a pre-arithmetical mechanism, to solve numerical problems through geometrical re-scaling. This foot based, fractional metrology then developed into the ancient metrology of Neal and Michell, which itself survived to become our historical metrology [Petrie and Berriman].

The two types of AMY, geometrical and the metrological, though not identical are practically indistinguishable; the AMY being just over one thousandths of an inch larger. The geometrical AMY (945/29 inches) is shown, by figure 2, to be geometrically resolvable, and so must have preceded the metrological AMY, itself only 40 thousandths of an inch less than the PMY.

The two AMYs, effectively identical, reveal a developmental history starting with day-inch counting, and division of 945 inches by 29 was made easy by exploiting the alternative factorisation of 32 PMV as 36 × 29 yards using geometry. The AMY of ancient metrology was the necessary rationalization of 945/29 inches into the foot- based system.

Bibliography for Ancient Metrology

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
  3. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  4. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  5. —-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016.
  6. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  7. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.

Astronomy 2: The Chariot with One Wheel


What really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth.

Extracted from Matrix of Creation, page 42.

Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. But the stars are lost in the brightness of the daytime skies and this obscures the Sun’s progress from human view. However, through observation of the inexorable seasonal changes in the positions of the constellations, the Sun’s motion can be determined.

The sidereal day is defined by the rotation of Earth relative to the stars. But this is different from what we commonly call a day, the full title of which is a tropical day. Our day includes extra time for Earth to catch up with the Sun before another sunrise. Our clocks are synchronized to this tropical day of twenty-four hours (1,440 minutes).

The Sun circumnavigates the zodiac in 365 tropical days, within which 366 sidereal days have occurred. There is one full Earth rotation more than there are sunrises within a year. This hidden oneness within the year is recapitulated in the one-unit difference between the number of sidereal days and the number of tropical days in a practical year.

The small catch-up time in every day is about three minutes and
fifty-six seconds long. This unit defines not only a sidereal day with 365 such units but also the practical year of 365 tropical days. The catchup unit is the difference between the duration of a sidereal day and that of a tropical day. It relates the Sun’s daily motion to the rotation of Earth and is a fundamental unit of Earth time (figure 3.6).

Figure 3.6. A polar view of Earth’s equator showing sunrises for two consecutive days. Compared with clock time, the stars rise three minutes and fifty-six seconds earlier each evening. (Drawn by Robin Heath)

THE MOON GATHERS THE TEN THOUSAND WATERS

The sidereal day (the duration of one rotation of Earth) is a very significant cosmic unit. The Jupiter synodic period of 398.88 tropical days is within 99.993% of four hundred sidereal days long. Therefore, twenty-five Jupiter synods (365 lunar orbital periods) equal 10,000 sidereal days since four hundred times twenty-five is 10,000.

A sidereal day differs from a tropical day due to the motion of the Sun during one tropical day. The three-minute-and-fifty-six-second time difference between these two days, the aforementioned catch-up unit, is quite useful when applied as the unit to measure the length of these days. A tropical day has 366 of these units while the sidereal day has 365 of the same units. The difference between the two is one unit.

Since 365 lunar orbits equal 10,000 sidereal days, it follows that a single lunar orbit has a duration of 10000/365 sidereal days. There are 365 units in a sidereal day, and therefore 10,000 units in a lunar orbit, so this new unit of time is 1/10000 of a lunar orbit. One ten-thousandth of a lunar orbit coincidentally is three minutes and fifty-six seconds in duration. The proportions in the Jupiter cycle combine with the lunar orbit, solar year, and Earth’s rotation to generate a parallel number system involving the numbers 25, 40, 365, 366, 400, and 10,000.

This daily catch-up unit I shall a chronon. Its existence means that the rotation of Earth is synchronized with both the lunar orbit and the Jupiter synodic period using a time unit of about three minutes and fifty-six seconds.

The sidereal day of 365 chronons is the equivalent of the 365-day practical year, the chronon itself is equivalent to the sidereal day, and so on. The creation of equivalents through exact scaling enables a larger structure to be modeled within itself on a smaller scale. This is a recipe for the integration of sympathetic vibratory rhythms between the greater and the lesser structures, a planetary law of subsumption.

The exemplar of the chronon was found at Le Menec: It’s egg-shaped western cromlech has a circumference of 10,000 inches and, if inches were chronons (1/365th of the earth’s rotation), then the egg’s circumference would be the number of chronons in the lunar orbit of 10,000. Dividing 10,000 by 366 (the chronons in the tropical day) gives a lunar orbit of 27.3224 – accurate to one part in 36704! The forming circle of Le Menec’s egg geometry provided a circumpolar observatory of circumference 365 x 24 inches, which is two feet per chronon versus the chronon per inch of the egg as lunar orbit.

The quantified form of the Le Menec cromlech was therefore chosen by the builders to be a unified lunar orbital egg, with a forming circle represented the rotation of the Earth at a scaling of 1:24 between orbital and rotational time.

The form of Le Mence’s cromlech unified the 10,000 chronon orbit of the Moon and 365 chronon circle of the Earth rotation because Thom’s Type 1 geometry naturally achieved the desired ratio. When the circle’s circumference (light blue) was 24 x 365 inches there were 10,000 inches on the egg’s. Underlying site plan by Thom, MRBB.

This design is further considered in Sacred Number and the Lords of Time, chapter 4: The Framework of Change on Earth, from the point of view of the cromlech’s purpose of providing a working model of the lunar orbit relative to the rotation of the circumpolar sky, leading to the placement of stones in rows according to the moon’s late or early rising to the East.

Capturing Sidereal Time


We can now complete our treatment of Carnac’s astronomical monuments by returning to Le Menec where the challenge was to measure time accurately in units less than a single day. This is done today at every astronomical observatory using a clock that keeps pace with the stars rather than the sun.

The 24 hours of a sidereal clock, roughly four minutes short of a normal day, are actually tracking the rotation of the Earth since Earth rotation is what makes all the stars move. Even the sun during the day moves through the sky because the Earth moves. Therefore, in all sidereal astronomy, the Earth is actually the prime mover. The geometry of a circumpolar observatory can reveal not only which particular circumpolar star was used to build the observatory but also the relatively short period of time in which the observatory was designed. Each bright circumpolar star is recognizable by its unique elongation on the horizon in azimuth and its correspondingly unique and representative circumpolar orbital radius in azimuth. …

The knowledge that was discovered due to the Le Menec observatory is awe inspiring when the perimeter of the egg shape is taken into account. It is close to 10,000 inches, the number of units of sidereal time the moon takes to orbit the Earth. The egg was enlarged in order to quantify the orbit of the moon as follows: every 82 days (three lunar orbits) the moon appears over the same part of the ecliptic. Dividing the ecliptic into sidereal days we arrive at 366 units of time per solar day.*

*These units are each the time required for an observer on the surface of the Earth to catch up with a sun that has moved within the last 24 hours, on the ecliptic, a time difference of just less than four minutes.

82 days times 366 divided by the three lunar orbits gives the moon’s sidereal orbit as 122 times 82 day-inches. Instead of dividing 82 by three as we might today to find the moon’s orbit, the pre-arithmetic of metrology enabled the solar day (of 366 units) to be divided into three lengths of 122. If a rope 122 inches long is then used 82 times (a whole number), to lay out a longer length, a length of 10,004 inches results. If 10,004 is divided by 366 units per day then the moon’s orbit emerges as 82/3 or 27⅓ days.

If a moon marker is placed upon the Le Menec perimeter and moved 122 inches per day, the perimeter becomes a simulator of the moon. …
Knowing the moon’s position on the western cromlech’s model of ecliptic and knowing which parts of the ecliptic are currently rising from the circumpolar stars enabled the astronomers to measure the moon’s ecliptic latitude.

Hence the phenomena related to the retrograde motion of the lunar orbit’s nodal period could be studied and its 6800 day length.

Astronomy 1: Knowing North and the Circumpolar Sky

about how the cardinal directions of north, south, east and west were determined, from Sacred Number and the Lords of Time, chapter 4, pages 84-86.

Away from the tropics there is always a circle of the sky whose circumpolar stars never set and that can be used for observational astronomy. As latitude increases the pole gets higher in the north and the disk of the circumpolar region, set at the angular height of the pole, ascends so as to dominate the northern sky at night.

Northern circumpolar stars appearing to revolve around the north celestial pole. Note that Polaris, the bright star near the center, remains almost stationary in the sky. The north pole star is constantly above the horizon throughout the year, viewed from the Northern Hemisphere. (The graphic shows how the apparent positions of the stars move over a 24-hour period, but in practice, they are invisible in daylight, in which sunlight outshines them.)
[courtesy Wikipedia on “circumpolar star”, animation by user:Mjchael CC-ASA2.5]

Therefore, the angular height of the pole at any latitude is the same angle we use to define that latitude, and this equals the half angle between the outer circumpolar stars and the pole itself. For example, Carnac has a latitude of 47.5 degrees north so that the pole will be raised by 47.5 degrees above a flat horizon, while the circumpolar region will then be 95 degrees in angular extent.

It is perhaps no accident that the pole is called a pole since to visualize the polar axis one can imagine a physical pole with a star on top, like a toy angel’s wand. The circumpolar region is “suspended” around the pole like a plate “held up” by the pole. Therefore, a physical pole, set into the ground, can be used to view the north pole from a suitable distance south (i.e., with the pole’s top as a foresight for the observer’s backsight). Such an observing pole would probably have been set at the center of a circle drawn on the ground, representing the circumpolar region around the north pole. This arrangement, a gnomon,* existed throughout history but usually presented as part of a sun dial.

*According to the testimony of Herodotus, the gnomon was originally an astronomical instrument invented in Mesopotamia and introduced to Greece by Anaximander. It was innovated even earlier, in the megalithic period, because structures that could operate one still exist within megalithic monuments.

It now appears a gnomic pole was also used in prehistory to locate the north pole in the middle of circumpolar skies. The north pole is opposite the shadow of the equinoctal sun at midday. The gnomic pole could also be used to find “true north,” as located halfway between the extremes of the same circumpolar star above the northern horizon. This can make use of the fact that when the sun is at equinox, it lies on the celestial equator and therefore is at a right angle to the north pole (see figure 4.4). This right angle is expressed at the top of the gnomic pole used and hence can enable the alignment of the pole through the similarity (or congruence) of all the right-angled triangles within the arrangement.

Figure 4.4. From pole to pole. It is possible to determine the angle of the north pole using a gnomic pole as shadow stick, but only at noon on the equinox. The laddie on the left cannot do this to a possible few minutes of a degree, but the geometry of the stick and shadow length can, providing true north and equinox alignments of east and west can be determined. Illustration on left from Robin Heath, Sun, Moon and Stonehenge, fig. 9.3.

Figure 4.4. From pole to pole. It is possible to determine the angle of the north pole using a gnomic pole as shadow stick, but only at noon on the equinox. The laddie on the left cannot do this to a possible few minutes of a degree, but the geometry of the stick and shadow length can, providing true north and equinox can be determined. Illustration on left from Robin Heath, Sun, Moon and Stonehenge, fig. 9.3.

To achieve an accurate bearing to true north, a circumpolar observatory can use the gnomic pole method, not just at noon on the equinox but every night, by dividing the angular range of circumpolar star, in azimuth. The north pole’s altitude, known to us as latitude on the Earth, can then be identified by dividing the angular range in altitude of a circumpolar star, a task achievable through geometry and metrology, so as to create a metrological model of the latitude upon the Earth.

It would seem obvious today that the pole star Polaris could have been used, but this is a persistent and widespread misunderstanding of the role of pole stars within the ancient and prehistoric world. Epochs in which there is a star within one degree of the pole are very rare and shortlived. Our pole star, Polaris (alpha Ursa Minor), is currently placed two thirds of a degree from a pole that is moving through the northern sky (figure 4.3 on p. 83) in a circle around the ecliptic pole of the solar system. Polaris will be nearest the pole (about ½ degree) at the end of this century.

The last time there was a star at all near the north pole was prior to the construction of the Great Pyramid in 2540 BCE . That pole star was Thuban (Alpha Draconis), and it was just one-fifteenth of a degree from the pole in 2800 BCE . The Great Pyramid has a narrow air shaft that pointed to Thuban, at which time it was already departing the pole and nearly one-third of a degree from it. Therefore, the megalithic people at Carnac, as well as almost all cultures throughout time, did not have the convenience of a pole star in approximately locating the north pole.

From 5000 to 4000 BCE , the time of megalithic building at Carnac, the north pole was a dark region surrounded by many bright stars. The inability to locate the north pole using a pole star challenged the people of the megalithic to develop a more sophisticated and accurate method. In any case, true north and latitude needed to be located more accurately than by using a pole star, which can only ever approximate the position of the north pole. Also, through the circumpolar observatory, sidereal time and even longitude between sites could be measured once the movement of the circumpolar stars could be exploited. True north, based upon these stars around the pole, can give the cardinal directions to an observatory.

The equinoctial sunrise in the east and sunset in the west can give a mean azimuth (horizon angle) to obtain south and north but only if the horizon is dead flat to each of these alignments. Far better then to observe the extremes of motion of a single circumpolar star, to the east and the west, to then find the North pole in between those two alignments.

Defining North by bringing the “clock in the sky” down to earth


One can therefore see that the circumpolar stars and sighting techniques, involving a gnomon, allowed north and the cardinal directions in a more reliable way than recording sunrise and sunsets since the sun on the horizon is variable between years due to the solar year having nearly ¼ day more than 365 days. The circumpolar stars enabled buildings and long sights to be built to true north-south-east-west, and by ignoring this, a building such as the Great Pyramid of Giza surprises us with its accurate placement relative to the cardinal directions.

From Sacred Geometry: Language of the Angels

from Sacred Geometry: Language of the Angels, Appendix 1.
(Available: first few weeks of 2021)
This is relevant to many on-site posts.

Metrology has appeared in modern times (phase five below) in reverse order, since humankind saw the recent appearance of many measures in different countries as indicative that past cultures made up units of measure as and when they needed them, perhaps based upon lengths found in the human body. But this soon breaks down under scrutiny because the measures called after different regions all have systematic ratios between them, such as 24/25 feet (which as a foot is the Roman) and 6/5 feet (which is an aggregate unit, a remen), and the size of humans is quite various between regions and within populations. As stated in the main body of this book, the notion of measures from different regions was called historical metrology. This framework began to break down when answers appeared as to why the different regional feet were related, not only to the English foot as equalling one for each ratio, but also to the fact that the units of measure were often seen to divide into the size and shape of the Earth (leading to our phase four)—then called ancient metrology.

Another aspect of measures was their ability to approximate important, otherwise irrational, constants (our phase 3), such as π, √2 and even e in the form of megalithic yards, which are close to 2.71828 feet, the numerical value of e—the exponential constant. The earliest megalithic yard was almost exactly that number of feet—derived from an astronomical count over three lunar and solar years in day-inches (chapter 1) leaving a 32.625-inch difference between these years (our phase one); those 32.625 inches equal 2.71875 (87/32) feet.

The gap between the first and second phases of metrology seems to be the gap in time between the megalithic in Brittany and in Britain. Only as the metrological purpose of more megalithic monuments becomes clear might one be able to know more accurately, but British metrology, in choosing a megalithic yard of 2.72, was able to factor the nodal prime number of 17 within its counting. While Brittany could, at Le Ménec’s western cromlech, use a radius of 17 megalithic rods (6.8 feet) to have a count of 3400 megalithic inches across a diameter, Britain could use 12 such rods to model the lunar year of 12 months while also counting 15 rods as 3400 shu.si, a small digit known to historical metrology as dividing the 1.8 foot (the double Assyrian foot of 0.9 feet) into 60 parts, while the shu.si (0.03 feet) divides into many foot modules (see p. 112), and the English yard contains 100 shu.si, and 68 yards contains 6800 shu.si enabling the nodal period to be counted at Balnuaran in Scotland.

There is a particular need to regularize this subject through the gathering of more examples of metrology’s past applications. One must recognize that those responsible for our present knowledge of it have largely passed away, and those in academia are not going to rewrite history in order to impartially reassess whether their own approach to ignoring it can still be justified, especially when they are not preserving the metrology within monuments because they can’t see it as a signal from the past.

Overview of Megalithic Units of Measure

At least five specific MYs have emerged from the counting applications within megalithic monuments:

1. The proto megalithic yard (PMY) of 32.625 day-inches, emanating from an original day-inch count over 3 solar and 3 lunar years (at the Manio Quadrilateral) as the difference in their duration (chapter 1). This is therefore an artifact of the world of inch counting.

2. The Crucuno megalithic yard (CMY) of 2.7 feet: We saw that, by the factorization of 32 lunar months as 945 days long, the lunar month (as 29.53125 days long) can be represented by 10 MYs of 2.7 feet (27 ft) where the days in such a count are the Iberian foot of 32/35 feet. This I call the Crucuno megalithic yard, though, in the historical period, this foot came to be called the root foot (27/25 feet) of the Drusian module, which, times 25, is then 27 feet. The astronomical megalithic yard AMY (next) is 176/175 of the CMY.

3. The astronomical megalithic yard (AMY): In Britain, this is 2.715 feet (32.585 inches) long, giving N = 32.585 for the actual N:N + 1 differential ratio between the solar and lunar years. When representing lunar months over a single year, the excess becomes the English foot of 12 inches—a megalithic, now-called English, foot. From this one sees that every AMY on the base of the Lunation Triangle defines an AMY plus 1 inch on the hypotenuse above it (length N + 1 = 33.585 inches – a Spanish vara), as the duration 1 mean solar month. The AMY can appear as an integer when the CMY defines a radius because it is 176/175 of the CMY.

4. The nodal megalithic yard (NMY): Used in Britain. Thom’s Megalithic Sites in Britain gave the megalithic yard as having had the value of 2.72 feet as “the” MY, based on integer geometries within stone circles and some statistical methods applied to some of the other inter-stone distances Thom had measured. Its value evidently derives from its relationship to the nodal period of 6800 day-feet because 2.72 =6800/2500, where 2500 feet is half a metrological mile of 5000 feet. For this reason, I now call it the nodal megalithic yard (NMY), which contains the key prime number 17 in its formula 272/100, 272 being 16 times 17. Its megalithic rod (NMY times 2.5) of 6.8 feet factorized the nodal period of 6800 days: 15 rods gave 102 feet (3400 shu.si) and 30 rods gave 204 feet (6800 shu.si – e.g. Clava and Avebury), the shu.si being 204/6800 = 3/100 feet. It therefore appears that the NMY, its rod of 6.8 feet, and the shu.si had a raison d’être in the British megalithic period that was focused on the later problem in astronomy of counting the days of the nodal period.

5. The later* megalithic yard (LMY): Seen at Stonehenge and Avebury. Thom in 1978 published a new estimate for the MY as 2.722 feet. Unbeknownst to Thom but lurking within his own error bars was a further development of the AMY which, times 441/440, would locate his value within ancient metrology as 2.716 feet, 126/125 of the CMY. The CMY is clearly the root value (in Neal’s terminology 2.5 root Drusian of 27/25 feet) and the AMY the root canonical value, while this LMY is the standard canonical value.
*in the context of Thom’s work.

All of these different megalithic yards had their place in the megalithic people’s pursuit of their astronomical knowledge. Noting the role of the shu.si in compressing the length of a nodal count to a mere 204 feet, Thom’s NMY of 2.72 is the key to how its length of 3/100 feet was arrived at. The shu.si of 0.03 feet (0.36 inches) surprisingly divides into many of the historical modules of foot-based metrology.

Historical
Module
Foot Ratioshi.siNotes
Assyrian 9/1030Carrying the sexagesimal (base-60)
system of the Sumerians.
Roman42/2532
Inverse Byzantine99/10033Times 3 gives 99, a yard minus one shu.si.
English133.3Times 3 gives 100 shu.si in a yard.
?51/5034Divides into the nodal period.
The difference between 80 and
81.6 feet and between 90 and
91.8 feet at Seascale, where 91.8
locates the Jupiter synodic period.
Persian21/2035Its remen (6/5) is 42 shu.si.
Drusian27/2536The CMY is root of the AMY and
the LMY.
Remen6/540Half-remen of 20 shu.si as ideal
form of the equal perimeter model.
Some units commensurate with the shu.si

Five Phases for Metrology

MetrologyThe application of units of length to problems of measurement, design, comparison or calculation. as a single system was based on the number 1, which was then realized astronomically as the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. as an excess over one year [Robin Heath, 1998; Heath & Heath 2010], which then became related to all the foot modules of the ancient world—through a range of simple fractions. There were, therefore, phases in the evolution of ancient and then historical
metrology. I can see five right away.

Phase One: An Inch-Based Metrology for Astronomical Counting*

Primordial measures arising from the conduct of astronomy in the megalithic period included the English inch used to count days at Le Manio, CarnacAn extensive megalithic complex in southern Brittany, western France, predating the British megalithic.; the Proto Megalithic YardAny unit of length 2.7-2.73 feet long, after Alexander Thom discovered 2.72 ft and 2.722 ft as units within the geometry within the megalithic monuments of Britain and Brittany. (PMYproto-megalithic yard of 32.625 (261/8) day-inches, generated at Le Manio Quadrilateral as the difference between three solar and three lunar year counts.) of 261/8 inches arising from Le Manio’s three-year count, forming the Lunation TriangleThe right-angled triangle within which the lengths of the two longer sides are the relative proportions of the solar and lunar years.; and the English foot arising from counting the Lunation Triangle over a single solar year as lunar months using the PMY per month.

To form the English foot required definite steps that were necessarily taken
through megalithic astronomy and findable in the monumental record as (a) the use of the inch to count days over 3 solar years,† (b) the use of the differential length over 3 years to count lunar months rather than days, and (c) the counting over a single year to find an excess length of the English foot, which still has 12 inches because the lunar year has 12 months.

*Corresponding to the work of Heath and Heath (2011) and Heath (2014)
†See “Reading the Angelic Mind” in chapter 1, p. 14.

Phase Two: A Foot-Based Metrology for Astronomical Counting‡


Using ad hoc simple foot ratios based upon the English foot, in the service of
astronomical counting such as: 27 feet representing the lunar month at Crucuno (near Carnac) enabling days to be counted in parallel, using Iberian feet of 32/35 feet; nodal units such as Thom’s early megalithic yard of 2.72 feet; and the yard of 3 feet containing 100 shu.si.§ Nearby, the use of feet per day can be seen at Erdevan, over the SarosThe dominant eclipse period of 223 lunar months after which a near identical lunar or solar eclipse will occur. and MetonicGreek: The continuous 19 year recurrence of the moon’s phase and location amongst the stars. periods. The full system of Ancient Metrology was not yet developed.

‡Corresponding to the work of Alexander Thom (1967, 1971, 1978, 1980)
§More on the types of megalithic yard and the shu.si can be found in the box above (p. 237)
called “Overview of Megalithic Units of Measure.”

Phase Three: A Foot-Based Metrology for Handling Mathematical Functions

Using ratios of the English foot to approximate to irrational and geometric functions: measures are able to map feet to √2 or its reciprocal, to π, or to other measures related to the models in chapter 2.

The English foot was long enough to form fractional ratios in which the number field could be expressed as a calculating tool, since the measurement of a length using a different ratio of foot length gives a result in which the original measurement has been multiplied by the denominator of the fraction and divided by the numerator. Thus, 9 feet becomes 8 feet of the ratio 9/8. The initial approach to such ratio-based feet was to build right triangles using English feet so that the foot of 9/8 feet emerged from a base length of 8 feet and hypotenuse of 9 feet. Above each foot on the base were 8 demarcated feet of 9/8 feet (see fig. 2.1, p. 34), and there are strong reasons to suspect grids of unit squares were in use to form triangles since the right angle is native to such grids, which are also conceptually adapted to studying pure numerical interactions in space.

Phase Four: A Metrology of Foot-Based Modules and Microvariations*

Foot modules evolved as a general-purpose toolkit involving only the prime numbers {2 3 5 7 11}: the systems of root measures using right triangular ratios from the common English foot standard; a common grid of microvariation within each module, applicable to geodeticUnits of measures and monumental measurements relating to the numerical definition of the shape of the Earth by the late megalithic. surveying and modeling; and some less common microvariations such as 225/224 and 81/80.

*Corresponding to the recent books about ancient metrology
from John Michell (1981, 2008) and John Neal (2000, 2016, 2017)

Phase Five: The Foot-Based Metrology Discovered from the Historical Period†

The historical measures were found through exploration of the geographical regions after which they were named, such as measuring sticks, anthropomorphic sculptures, objects whose size was noted in antiquity, modern-era survey measurements (e.g., by Petrie and Thom), and through inductive metrology, measuring surviving sites and artifacts.

†Corresponding to Petrie (1877) and Berriman (1953)

BIBLIOGRAPHY

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
  3. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  4. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  5. —-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016.
  6. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  7. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.

The Discovery of a Soli-Lunar Calendar Device at Le Manio

by Robin Heath

In 2009 I returned to Plouharnel, again for the Solstice Festival, and undertook my own research both before and after the four day event. Howard Crowhurst had undertaken a great deal of theodolite and tape work at a well known site called Le Manio. This collection of surviving monuments forms an exceptionally rich group of astronomical alignments which together carry enormous ritual significance in that these sites hold information about human conception, the gestation period and ritual use of geometry and metrology. Howard understands the site to the point where his three hour workshop covered much of this material, and the implications of it were clearly understood by non-specialists. Those readers who have the chance to attend the Festival, and who speak either English or French, should regard this experience as a megalithic ‘must’. Howard is an exceptionally good communicator of what are often seen as difficult areas of megalithic research, and he is astonishingly good at passing these ideas on to his audience with a great deal of clarity, enthusiasm and humour.
It was during Howard’s seminar/workshop that he invited me to set up his theodolite within the Le Manio Quadrilateral, a curious site near the 6.5 metre high ‘Giant of Le Manio’. This done, I noticed something I had been searching for for twenty years. Read on…!

Le Site Mégalithique du Manio à Carnac

by Howard Crowhurst

Perched on a hill in the forest north of the Carnac alignments, a megalithic site has escaped the fences that have littered the landscapes of the region for several years. These are the menhir and the quadrilateral of Manio. From the outset, the large menhir impresses with its dimensions. Nearly 5m50 high, it is the highest standing stone in the town.

More discreet, the quadrilateral caps the top. 90 upright and contiguous stones, varying in height between 10 cm and 1m60, make up an enclosure approximately 36 meters long and 8 meters wide on average, because the long sides converge. The stones at the ends draw a curve. Four stones to the northeast form the remains of a circle. Two menhirs, much larger than all the other stones in the quadrilateral, open a kind of door in the south file. This particular form questions us. What could she be used for? Was it a meeting place, maybe an enclosure for sheep? In fact, what we see today is probably only the outer skeleton of a larger monument, a mound of stone and earth that contained a chamber inside. Other remains complicate the whole, unless they help us solve our puzzle. Hidden in the brambles and brush, we can discover a stone on the ground of rounded shape. These curves are reminiscent of the belly of a pregnant woman. She is nicknamed the “Lady” of the Manio.