from Sacred Geometry: Language of the Angels, Appendix 1.

(Available: first few weeks of 2021)

This is relevant to many on-site posts.

MetrologyThe application of units of length to problems of measurement, design, comparison or calculation. 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 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 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 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. 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 cromlechBreton word for a rounded kerb monument or stone circle., 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 periodUsually referring to the backwards motion of the lunar orbit's nodes over 6800 days (18.618 years), leading to eclipse cycles like the Saros. 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 (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 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 (CMYCrucuno megalithic yard of 2.7 feet, crucial to the factorization of time where 10 CMY become a lunar month of 945/32 days of 32/25 feet per day, the Iberian foot.) 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 AMYA megalithic yard which, in inches, expresses the true astronomical ratio of mean solar months to lunar months. (next) is 176/175Ratio crucial to maintaining integers (see geometry lesson 2) between radii and circumference of a circle, and crucial to the micro-variation of foot modules in ancient metrology. 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 TriangleThe right-angled triangle within which the lengths of the two longer sides are the relative proportions of the solar and lunar years. 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 Ratio | shi.si | Notes |

Assyrian | 9/10 | 30 | Carrying the sexagesimal (base-60) system of the Sumerians. |

Roman | 42/25 | 32 | |

Inverse Byzantine | 99/100 | 33 | Times 3 gives 99, a yard minus one shu.si. |

English | 1 | 33.3 | Times 3 gives 100 shu.si in a yard. |

? | 51/50 | 34 | Divides 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 synodicThe recurring time cycle of a given celestial phenomenon seen from the Earth. period. |

Persian | 21/20 | 35 | Its remen (6/5) is 42 shu.si. |

Drusian | 27/25 | 36 | The CMY is root of the AMY and the LMY. |

Remen | 6/5 | 40 | Half-remen of 20 shu.si as ideal form of the equal perimeter model. |

## 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 CarnacAn extensive megalithic complex in southern Brittany, western France, predating the British megalithic.) 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

- Berriman, A. E.
*Historical Metrology*. London: J. M. Dent and Sons, 1953. - 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*. - Michell, John.
*Ancient Metrology*. Bristol, England: Pentacle Press, 1981. - Neal, John.
*All Done with Mirrors*. London: Secret Academy, 2000. - —-.
*Ancient Metrology*. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016. - —-.
*Ancient Metrology*. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017. - Petri, W. M. Flinders.
*Inductive Metrology*. 1877. Reprint, Cambridge: Cambridge University Press, 2013.