The megalithic yard, a unit first proposed by Alexander Thom in the mid twentieth century, remains one of the most provocative ideas in the study of prehistoric measurement. Thom’s surveys of stone circles across Britain suggested the use of a standard unit of measure. His conclusions, although debated, invited a reconsideration of what prehistoric geometry may have represented and how ancient builders and engineers may have linked their monuments to cycles of time and astronomy.

Professor Thom approached the problem of prehistoric geometry with an engineer's mind, and a surveyor’s precision. Thom compiled thousands of measurements from stone circles across Scotland, England, Wales and Brittany. In Megalithic Sites in Britain (1967) and Megalithic Lunar Observatories (1971) he concluded that “there existed a standard unit of length which the builders used with considerable accuracy” and that this unit, the megalithic yard, had a value of 2.72 feet, 32.64 inches or 0.829 metres. Thom drew attention to the remarkable consistency of this measure in monuments separated by hundreds of miles, stating that “the same unit recurs with such frequency that chance cannot account for it.”

The clearest expressions of the megalithic yard appear in stone circles with large numbers of uprights. Thom frequently cited the circles of Callanish and Stenness, as well as the great rings at Avebury and the recumbent stone circles of northeast Scotland. In Brittany, he identified the same measure in the alignments of Carnac and in the diameters of several passage graves. His statistical treatment led him to conclude that the megalithic yard was “not merely a convenient approximation but a deliberate standard” which was subdivided into forty or fifty equal parts. Although Thom's analysis is largely ignored, the dataset itself remains impressive. The recurrence of Thom’s value within both British and French monuments has ensured that the megalithic yard continues to receive serious consideration, particularly when viewed in relation to astronomical cycles rather than isolated architectural dimensions. Does the megalithic yard encode a reconciliation of solar and lunar time through circular geometry?

The Metonic cycle

There are various numbers of solar or tropical years which reconcile quite well with integer numbers of synodic lunar months. The Metonic cycle is one such period, and is 19 years of 365.242199 days, or 235 synodic months of 29.53059 days long. In addition to this, it also reconciles the sidereal month of 27.321661 days to these other two cycles. So:

235 x 29.53059 ≈ 19 x 365.242199 ≈ 254 x 27.321661

The Metonic cycle was in use historically, and four Metonic cycles combined together increased the precision of the reconciliations further, and were known as the Callipic cycle. In particular, the Metonic cycle was used in the Antikythera mechanism, a Greek device of the second century BC used for calculating planetary and lunar positions. This mechanism relied upon the ratio 254 / 19 to model the Metonic cycle.

The Fraction 254/19 in the Antikythera Mechanism

The Antikythera mechanism, recovered from a first century BC shipwreck is the oldest known geared astronomical calculator, and incorporates within its gearing the ratio 254/19, a fraction used to approximate the Metonic cycle. Modern analyses, particularly those of Freeth, Jones and their collaborators, have shown that the Metonic pointer is driven by a train built around the relation between lunar and solar cycles. In the words of Freeth et al. (Nature, 2006), “the designers employed a 254 to 19 gearing relation in order to model the 19 year lunar cycle with remarkable fidelity”. This ratio appears as a practical integer approximation of the more precise figure of 235 lunations in nineteen years, allowing the mechanism to advance its lunar calendar at the correct rate without relying on irrational numbers. The recurrence of the nineteen year cycle, the same period employed in the construction of your Metonic circle model, demonstrates how strongly the Metonic system lay at the heart of ancient astronomical practice.

The presence of 254/19 in the mechanism is embedded in the gear work such that each turn of the solar pointer results in the appropriate advancement of the lunar calendar disc. The Antikythera device therefore provides an independent, Hellenistic attestation of the Metonic ratio as a structuring principle of astronomical design.

The 19/254 ratio

Reversing that ratio, 19 / 254, and applying it to the geometry of the circle, and the metre may provide a clue as to what the megalithic yard is about. The megalithic yard can be interpreted as the circumference of a circle with a diameter of 19 metres divided into 72 parts. That gives a value of 32.639 inches, with the value for pi given by a calculator. In metres 19π/72 is 0.82903. This is close to 12⁴ x 4/100 000 metres. The circle with a diameter of 19 metres has the advantage of linking the unit of measurement to astronomy, which is interesting as it fits with the idea of many megalithic monuments being linked to astronomy. Dividing the circumference into 72 equal parts resonates with harmonic numbers, and precessional numbers (divisions of the 25920 year cycle).

To obtain the value for the megalithic yard in inches, i.e. to convert the above equation to inches from metres, you need to multiply by 100 000 / 254.

19/254 π x 100 000 / 72 = 32.639 inches.

As noted above, 254 is the number of sidereal months in a Metonic period. And 19/254 is reminiscent of the 254/19 ratio present in the Antikythera mechanism.

This provides a case for saying that the metre, the inch and the megalithic yard relate to astronomy, in a prehistoric context, and to the Metonic cycle in particular, and the need to reconcile the cycles of the sun and moon. If we consider the metre as a fundamental unit of measure, the megalithic yard may be understood as the product of this unit and the geometry of the circle within a broader cosmic design. 19π / 72, equals 0.82903 metres, a figure tantalisingly close to Thom’s 0.829 m. The metre, a rationalisation of the earth’s polar circumference, provides the geometric framework in an attempt to bind celestial rhythm to terrestrial form through number, proportion and geometry. the inch brings in the number 254 to the equation, linking it to the Metonic cycle via the sidereal month.

The lunar and solar logic behind the metre and the inch

If the metre is about the polar circumference, being roughly a 40 00 000th part of it, the inch is about the equatorial circumference. This insight was, as far as I know, first put forward by Robyn Heath in the Lost Science of Measuring the Earth, co-written with John Michell. According to his view the circumference can be understood as 365.25 x 360 000 English feet (or 365.242199 x 360 000 feet). Another way of expressing the connection between the inch and the polar circumference is through the period of time of 4 320 000 years known as the yuga, in the Indian tradition. So the circumference becomes 4 320 000 x 365.25 inches (or 4 320 000 x 365.242199 inches). A point on the equator thus travels 4 320 000 x 365.25 inches in 365.25 days, in relation to the axis of the earth (not in relation to the stars or the sun).

The division of the equatorial circumference into 4 320 000 x 365.25 parts, and the division of the polar circumference into 40 000 000 parts, happen to be reconciled through the geometry of the circle and the reconciliation of the solar and lunar circles through the Metonic cycle. By a strange coincidence, a circle with a diameter of 1000 x 29.53059 has a circumference of very nearly 254 x 365.242199 units (29.53059 is the synodic month in days, 365.242199 is the solar year in days). So, when the diameter of the circle is set to one thousand synodic months, expressed in days, the circumference corresponds almost exactly to 254 solar years, also expressed in days, using calculator pi. Pi somehow brings the Metonic numbers together. 19 is the number of years, 254 is the number of sidereal months, 235 is the number of synodic months.

19π x 1000 / 254 = 235.001

29.53059×π×1000 / 365.242199 ≈ 254

365.242199×10 / (29.53059 π) ≈ 39.37 

That 39.37 is the number of inches in a metre, so close that it suggests a deliberate relationship between the lunar cycle, the solar year, and the interplay of diameter and circumference in a circle (pi).

If a circle is drawn with a diameter of 35.436708 metres, its circumference becomes 365.24836 imperial feet, which is approximately the solar year. The geometry echoes the solar and lunar equation:

365.24836 / π=35.436708 

There is an interesting set of numerical relationships that appears when one compares the structure of the metre with the behaviour of lunar and solar cycles. If we take the ten thousandth part of the polar meridian quadrant, which is one thousand metres, and multiply it by the length of the lunar year expressed in days, 354.36, and by the value of pi, then divide the result by 254 and by 12, the outcome is 365.24107, very close to a year in days. The same value is obtained if the polar quadrant is divided by one hundred million to give a measure of one tenth of a metre, then multiplied by 354.36 and pi, as the result is again 365.24107, now expressed in feet. A further variation, in which the polar quadrant is divided by one hundred thousand, multiplied by the lunar year and by pi, and finally multiplied by 360, produces a result close to the equatorial circumference expressed in metres.

If we divide the polar quadrant by 10⁵, multiply by the number of days in a lunar year (354.36) and by π and by 360, we obtain a very good approximation to the Earth’s equatorial circumference in metres.

Equatorial circumference ≈ Polar quadrant x lunar year x 360 π / 10⁵

By definition the meridional quadrant is 10 million metres, though estimates suggest this is slightly off. When you fold in the lunar year and the angle of a full circle, the same polar quadrant gives, almost exactly, the equatorial circumference in metres.

The polar meridian divided into roughly 40 million parts to produce the metre, and the equator divided into roughly 4 320 000 × 365 inches, are then two faces of a single scheme, brought into accord through factors like 354.36 and 254 which belong to the reconciliation of solar and lunar time in the Metonic tradition. In this view the metre and the inch are not rivals from two historical measurement systems but paired expressions of the same schema. Geometry offers a natural medium for reconciling the cycles of the sun and moon. Both units can therefore be interpreted as calendric lengths, emerging from a worldview in which number, astronomy, and geometry form a coherent whole. This is the intellectual world in which the Metonic cycle, the megalithic yard, and, the mechanisms such as Antikythera all seem to participate.

We can only wonder if the value of the megalithic yard expressed in feet, as 2.72, is made to encode the draconic month of 27.2122 days.  If this resemblance is intentional, even approximately so, it would place the megalithic yard within the family of lunar constants that structure the geometry of eclipses. A length that evokes the draconic cycle would be a very deliberate choice for any system concerned with reconciling solar and lunar time, for the draconic month governs the points at which the Moon’s path crosses the ecliptic and thus determines when eclipses may occur. Whether this echo is numerically designed or arises as a by-product of using sixty eighths of a nineteen metre circle, it reinforces the impression that the megalithic yard, however we define its exact origin, sits at the intersection of geometry and celestial cycles, and that its apparent simplicity is layered with astronomical meaning.

In Geoff Bath's excellent book Stone Circle Design and Measurement, Standard Units and Complex Geometries, there is a table with the diameters of the many circles surveyed by the author, given in metres. Only one measures 19 metres in diameter, and this is Yonder Bognie, in Scotland. Merrivale SE has a diameter of 19.1 metres. There is a huge variety of measures in the size of stone circles generally, with a handful of repeating numbers, such as diameters of 3.1 and 3.2 metres, and 31.5 or 31.6 metres. But there is certainly no pattern of circles with diameters of 19 metres. Curiously, however, the circles with diameters of 3.1 metres would produce circumferences of 235/20 inches if the diameters were in fact 3.101 metres. 235 is the number of synodic months in a Metonic period. So it's possible that the 3.1 metre diameter, present in 11 circles in Geoff Bath's table, also have a Metonic connection.

 The juxtaposition of Thom’s findings with the Metonic framework offers an interesting, if speculative interpretative lens. If the megalithic yard represents the division of circle with a diameter of 19 metres into seventy two parts, then Thom’s empirical discovery may be understood not simply as a constructional convenience but as a geometric abstraction of the reconciliation between the lunar and solar year. The megalithic yard thus becomes a bridge between celestial motion and human scale, between the cycles of the heavens and the measures of the earth. It is therefore reasonable to regard the megalithic yard as a luni-solar measuring quantum, derived from the same mathematical harmonies that gave rise to the inch and metre.

Bibliography

Bath, Geoff. Stone Circle Design and Measurement, Standard Units and Complex Geometries 2: Stylised Plans and Analysis of over 300 Rings. Key Press, UK, 2021.

Chamberlain, Andrew & Pearson, Mike Parker. “Units of Measurement in Late Neolithic Southern Britain.” In Larsson, M. & Parker Pearson, M. (eds) From Stonehenge to the Baltic: Living with Cultural Diversity in the Third Millennium BC, BAR International Series 1692. Archaeopress, Oxford, 2007, pp. 169–174.

Heath, Robin & Michell, John. The Lost Science of Measuring the Earth. Adventures Unlimited Press, 2006

Thom, Alexander. Megalithic Sites in Britain. Oxford University Press, 1967.

Thom, Alexander & Thom, Archie. Megalithic Remains in Britain and Brittany. Clarendon Press, Oxford, 1988.

Freeth, Tony, et al. “Decoding the Ancient Greek Astronomical Calculator Known as the Antikythera Mechanism.” Nature 444 (2006): 587–591.