This is all that remains standing or marked in the southern ring at Avebury, although English Heritage lists other extinguished positions in its electronic map. At some future point the merits of those positions can be added to this analysis, but at the moment we'll concentrate on what is visibly marked by surviving obelisks or concrete plinths.


The distance is 170.1' - 1701/10 and the return angle to the obelisk is 99°.

Professor Alexander Thom and other surveyors have accepted that the defining diameter of this southern circle was 340 feet. The true diameter was intended to convey 340.2 - 3021/5' (radius 170.1'), as this was a special value that related directly to the duration of the lunar nutation cycle (6804-days), where the moon moves from Major standstill to minor standstill and back to major standstill. The duration of 3402-days represents the period from Major to Minor standstill. The value is symbolically encoded (in enlarged form) into the base dimensions of the Khafre Pyramid. It will be remembered that the Khafre base measurement @ 708.75 - 7083/4' per side was 2835' for one complete circumnavigation. In inches this is 34020.

The 99° return angle is in homage to the "11" series of measurement increments, including the league (16500'), the mile (5280'), the furrowlong or furlong (660'), the chain (66'), the rod or perch (16.5'), the fathom (originally 5.5'), the link (7.92 - 723/25").

A second reading of the position (on the other end of the original stone?) could have meant a distance of 172.8'. This was one of the most important values of antiquity and related directly to navigation at sea using the mile of 5280' for linear distances or legs of travel. The value was built into the circumference of Silbury Hill in the base diameter and circumference. In one cross measure of Silbury Hill's base the intended diameter appears very strongly to have been 550' (100 ancient fathoms or modern merchant navy fathoms). Using PI @ 3.141818182 (1728/550) this converts to a circumference of 1728'. The value produced is purely "6" based and works perfectly within a 360° environment.

The navigational principle being exploited by this "window" of opportunity in using PI was that linear distances (traversed) using an "11" series number would convert to a sexagesimal circumference, thus making positional plotting of each sea-leg covered easy to do despite many course changes in zigzagging to a destination.

The return angle for this second reading was 98.4375° (987/16ths) and this related to the lunar month. The sum of 9.84375-days (927/32nds) was one third of a lunar month of 29.53125-days (2917/32nds).

1 Talent………….590625.0 grains equals: 1 Talent………….590625.0 grains equals:
60 Mina………….9843.75 grains, or 60 Mina………….98433/4 grains, or
3000 Didrachma…196.875 grains, or 3000 Didrachma…1967/8 grains, or
6000 Drachma……98.4375 grains. 6000 Drachma……987/16 grains.


The distance is 165' or 10 rods and the return angle is 86.4 - 862/5°.

The distance value is in homage to the "11" family of measurements. The sum of 165' would be 100th of a league @ 16500' (3.125 - 31/8 miles). This distance at Avebury would also be 2.5 chains, 30 merchant navy fathoms, 10-rods or 250 links.

The angle of 86.4 - 862/5° (half of 172.8) provided a a very important tutorial for navigation by the "11" family of numbers.

A former mound, which has been plowed over by millenniums of farmers, is still highly visible after harvest. This situation prevails all around the Avebury district and many such vivid field markings, where humped up ancient mound structures were precisely placed, can still be detected seasonally. Other mounds had large stones on them and these have survived in far better condition, as they represented a major obstacle to the farmer's plough. This mound is situated at Lat: 51.434660 , Long: -1.925016.

This mound sat exactly 1-league (3.125-miles or 16500') from the giant obelisk at Avebury Henge at an azimuth angle of 98.4375° (987/16ths) back towards the henge. The degree angle code is lunar and 9.84375-days (927/32nds) would be exactly 1/3rd of a lunar month of 29.53125-days (2917/32nds solar days).


Again, the distance is 170.1 - 1701/10' in homage to the lunar nutation cycle.

The angle back to the obelisk is 74.25°, which is based upon an increment of 2.475 (219/40ths). Remember that the equatorial size of the Earth was 24750-miles under the Great Pyramid's second navigational assignment that used "11" number family values. The "Y" Holes circle at Stonehenge (178.2') was 72 increments of 2.475' (29.7") in diameter. The same holds true for "Z" Holes at Stonehenge where the diameter is 132' (2.475 X 64). Mathematical progressions culminating in the number 891 (2.475 X 360) occur in the decipherable measurements and angles scattered from the Eastern Mediterranean and Europe to Nazca, Peru and Easter Island. The progression seems to have been very popular in navigational computations.


For the first time in this analysis we have the opportunity to work across a very large original standing component. This provides a glimpse into the fact that each of these outer markers from the central obelisk were multicoded from the left to right side extremities across the face. Placing a 40-100 ton boulder into an exact position was no small undertaking and it would be the desire of the builders & teachers to encode several tutorials into any one position. Let's consider 4 obvious tutorials identifiable in this stone's position.

(a). To the northern edge of the stone the distance is 168' and the return angle is 64°.

HEBREW CUBIT OF A MAN (decimal fraction). HEBREW CUBIT OF A MAN (fraction).
1 Cubit….. 16.8 inches equals: 1 Cubit….. 164/5 inches equals:
2 Span….. 8.4 inches, or 2 Span….. 82/5 inches, or
4 Hand…. 4.2 inches, or 4 Hand…. 41/5 inches, or
24 Finger…. .70 inches. 24 Finger…. 7/10 inches.

The 168 value was highly important both navigational and lunar computations. Under the 24883.2 Greek mile equatorial circumference system found in the literal dimensions of the Great Pyramid's base, 1-second of arc was 100.8 - 1004/5' (the same as the diameter of Stonehenge's Sarsen Circle in one internal cross measure. One 6th part of 1-second of arc would be 16.8'. At Stonehenge the Aubrey Circle positions were determined by 3,4,5 triangulation* (using ropes). The triangle had an adjacent of 126', an opposite of 168' and a hypotenuse of 210'.

*Note: This use of ropes to form a huge 3,4,5, triangle (that could be swiveled through 360° of arc) and make angle computations therefrom also occurred at the Sanctuary Circle, South of Avebury Henge. In that case the 3,4,5 triangle had sides of 105' (adjacent), 140' (opposite) and 175' (hypotenuse). See Articles 7 & 8 in this series.

The 168 value was also very important to computations within the lunar and solar cycles. There are 168 hours in a week.

The value of 64 (8 X 8) was highly important to calculations and that seems to have been the original purpose of the ("out of Egypt") chess board. The Druidic Calendar of Coligny was set out as 128 half squares or 64 squares, including 2 intercalary sections for optional use, depending if one was following either the solar or lunar cycles. The plaque worked to 1890-days (note: the 756' length of the Great Pyramid is 189' X 4). To monitor the solar period the calculation was 1890 ÷ 63 = 30-days (solar month). For the lunar period it was 1890 ÷ 64 = 29.53125-days (2917/32nds).

(b) Coming in towards the centre face of the stone the distance is 161.804' (PHI coding) and the return angle is 63°.


1 Talent….378000 grains equals:
60 Mina…6300 grains, or
80 Libra…4725 grains, or
960 Uncia…393.75 grains.

The distance, of course, encodes the PHI ratio (1.6180339 to 1). The importance of this value to ancient society cannot be overstated and, amongst other things, it was at the heart of all computations related to capacities built into round volume tubs that were used by merchants in the ancient market places. See Footnote 1

(c) Slightly south of the centre face the distance is 162' and the return angle is 62.5°.

The 162' is indicating "rounded" PHI and Professor Alexander Thom's discovery of a repetitive interval at Stonehenge was probably an increment of 32.4" in ancient society.

The angle of 62.5° would code a base increment related to navigation using the "11" family of numbers. Under that system 1° of arc was 68.75 - 683/4 miles of which 6.25-miles would be 1/11th.

(d) To the southern edge of the stone the distance is 166.666' and the return angle is 60.75 - 603/4.

In any 3,4,5 triangle the shortest side adjacent to the hypotenuse is 1.66666666 less in length, whereas the side opposite the hypotenuse is 1.25 less in length.

The 60.75 return angle codes a lunar value. There would be 60 .75 periods of 42-days in the 2551.5-day lunar count monitored within the Sabbatical calendar system.


5(a) The distance is 165' (10- rods) and the return angle is 51.84° (the slope angle of the Great Pyramid).

5(b). The distance is 162' and the outwards running angle is 230.4° (return 50.4°).

GREEK VOLUMES…LIQUID (decimal fractions). GREEK VOLUMES…LIQUID (fractions).
1 Metretes…2332.8 cubic inches equals: 1 Metretes…23324/5 cubic inches equals:
12 Chous…..194.4 cubic inches, or 12 Chous…..1942/5 cubic inches, or
144 Cotyle…16.2 cubic inches, or 144 Cotyle…161/5 cubic inches, or
576 Oxybaphhon…4.05 cubic inches, or 576 Oxybaphhon…41/20 cubic inches, or
864 Cyathus…2.70 cubic inches. 864 Cyathus…27/10 cubic inches.

This length relates, once again, to "rounded PHI " , but could also have been read as 161.80339' in order to provide a tutorial concerning the PHI ratio.

The degree angle is navigational and identifies a value in a very important ancient mathematical progression used universally by the Caucasoid cousin nations. The progression goes 1152, 2304, 3456, 4608, 576, 6912, 8064, 9126, 10368, etc.

At Stonehenge there was a ring composed of 30 lintels on the Sarsen Circle and the outer rim circumference @ 345.6' averaged 11.52' (1113/25ths) per lintel stone length. Similarly, the Great Pyramid was built as a truncated pyramid with a flat floor altar on top. The diagonal distance from the base up to the edge of the top altar floor was coded to be 576'. Alternatively, the vertical height was coded to be 453.6'.

5(c) The distance is 166.66666' and the angle is 48°.

This length is simply 1/3rd of 500'. The 1: 1.6666666 ratio was very important in understanding the geometry of the 3.4.5 triangle.

The degree angle identifies one of the most used values of antiquity, which related to navigation and other calculation functions.

5(d). The distance is 165' and the angle is 47.25°

The Great Pyramid's base length (756') = 16 X 47.25'. The Khafre Pyramid's base length (708.75 - 7083/4') = 15 X 47.25'. Khafre's design height was 472.5'.


The distance is 162° and the angle is 36.66666666°.

The value 36.666666' is merely 1/3rd of 110'. It's probable that from this position a tutorial about 36.525 (36 & 21/40ths) would have discussed the duration of the solar year (365.25-days).

The distance is 165' and the angle is 36°.

The ancient sexagesimal compass was based upon a circuit of 360°.


The distance is 165' or 10-rods to the northern side of the stone and the angle from the obelisk out to this side position is 207.36° - 2079/25.

The angle value introduces the Egyptian Royal cubits of which there were 3 very closely similar types. The largest was 20.736" long (1.728' - 191/125... there are 1728 cubic inches in a cubic foot) and each of the three types was fashioned for mnemonic recall related to the size of the Earth under one of 3 different equatorial circumference systems. See Footnote 2.

(b) The distance to the centre face of the stone is 162' at an azimuth angle back to the obelisk of 24.3°.

The distance is, of course, homing in on "rounded" PHI @ 1.62. In one circumnavigation of the Great Pyramid the "inch" value (756' per side) was 36288". This distance is 2240 rounded PHI inches of 1.62".

The angle of 24.3° return provides dynamic lunar & navigational coding simultaneously and represents a value within one of the most important mathematical progressions of antiquity. For example: the lunar nutation cycle of 6804-days is 28 periods of 243-days. Similarly, the 2551.5-day lunar period (7.2 lunar years) monitored within the lunisolar Sabbatical calendar system was 10.5 periods of 243-days.


(a) The distance is 165' and the angle is 14.66666°.

Once again the distance is focusing on the "11" series of navigational numbers and this length would be 30 ancient fathoms or 10 rods (1/32nd of a mile @ 5280'. The angle to the western side of the stone is 14.66666° and this also is a navigational mathematical progression from the "11" family of numbers (the sum of 14.666666' would be 1/360th of a mile).

(b) The distance is 162' and the angle is 12.375 - 12 3/ 8°.

This vector to the central region of the stone's face is again accentuating PHI and "rounded" PHI values. A mathematical progression based upon 162 was useful in navigational, lunar and Precession of the Equinoxes calculations simultaneously.

The degree angle (123/8ths) was navigational coding and would have provided the tutor with the opportunity to teach up to five systems related to the equatorial size of the Earth and how to do positional plotting at sea based upon each system. In a world considered to be 24750-miles in circumference ("11" system), half of that value would be 12375-miles. For a world considered to be 24883.2-miles in equatorial circumference (12 X 12 X 12 X 12 X 1.2-miles) the half value would be 12441.6-miles, etc.

1 Cor…….22394.88 cubic inches equals, 1 Cor…….2239422/25 cubic inches equals,
10 Bath….2239.488 cubic inches, or 10 Bath….223961/125 cubic inches, or
60 Hin…..373.248 cubic inches, or 60 Hin…..37331/125 cubic inches, or
180 Cab…124.416 cubic inches, or 180 Cab…12452/125 cubic inches, or
720 Log…31.104 cubic inches. 720 Log…3113/125 cubic inches.

(c) The distance is 166.666666 - 1662/3' and the angle is 9.9°.

The distance is simply 1/3rd of 500'. In any 3,4,5 triangle the hypotenuse will be 1.666666 longer than the adjacent.

The degree angle is merely accentuating the values of the "11" system of navigational numbers once again.


(a) The distance is 165' and the angle is 2.88°.

Again, a reading of 165' (10 rods) is achievable to the western side of the stone.

The degree angle (222/25ths) homes in on one of the most important values of antiquity (288) used in all manner of navigational and Precession of the Equinoxes calculations. It was also used in area standards and the Egyptian Pyramid Acre was 28800-square feet.

(b) The distance is 160' and the angle is 1.18125 - 129/160 °.

The distance would be 1/33rd of a mile and a progression based upon 160 would be very useful in navigational calculations. Our ancient 360° compass system divides very effectively into 1/16th and 1/32nd increments.

The angle from this centre face position to the obelisk would have carried a lunar cycle tutorial based upon 129/160 .

(c) The distance is 161.804' and the angle is 0°.

The distance to the eastern side of the stone coded the PHI ratio value in expanded form (X 100).

The 0 to 180° line (true North-South) provided a way to set theodolites or alidade sighting rules onto a fully correct orientation before fixing upon secondary targets around the henge or more distant skyline (including star or planetary positions, etc.).


(a) The distance is 229.166666666 and the angle is 166.666666666°.

The 229.1666666 (2291/6th) value was important to navigational calculations under "11" the geodetic system that considered the Earth to be 24750-miles in circumference. The progression produces values like 6875 (1° of arc under the 24750-mile circumference was 68.75 - 683/4 miles).

The angle from the obelisk to this position is 166.66666° (1662/3rds), again accentuating this very useful value or ratio.

(b) The distance is 230.4' and the angle is 345.6°.

The 2304 value (1152 X 2) was highly important to navigational mathematical progressions or for lunar cycle duration calculations. At Stonehenge the outer rim of the Sarsen Circle of lintels was meant to convey a circuit of 345.6' or 30 X 11.52' (15 X 230.4'). The coding on the lintels related to both the equatorial size of the Earth and the duration of the lunar nutation cycle simultaneously. Thus: The sum of 345.6-miles would be 1/72nd of the Earth's circumference in a world that was 12 X 12 X 12 X 12 X 1.2-miles around (24883.2-miles).

Similarly, the lunar nutation cycle takes 6804-days to complete, which equates to 230.4 lunar months.

We must remember that the stone positions represented teaching opportunities and that several tutorials would have been encoded into each stone. These monuments were mnemonic devices and there was a very strong reliance on the knowledge of generations of learned tutors when extracting the precise information contained within each stone. It is agreed that the positions of rough hewn or irregular stones could not have achieved the distance and angle precision mentioned above. The builders who erected the monuments stood them as close as was humanly possible to the precise positions that would indicate the intended, encoded information, but the refinements (down to fractions of an inch or degrees of arc) came from the tutor's profound knowledge and experience.

Footnote 1.

For a king or provincial governor/ priest, trying to keep peace within regional society, few things were more threatening to harmony than "short measures" being meted out in the market place. This problem has required eternal vigilance, worldwide, since time immemorial. The responsibility to know what constitutes a correct measure in weight, volume or length, as well as the enforced maintenance of precise standards, was always a primary function of localised leadership.

The original bushel of England was, undoubtedly, directly related to a Sumerian/ Babylonian volume called a Homer, which was 21600 cubic inches. The English Winchester bushel of recent centuries was 2150.42 cubic inches or very close to 6 X 6 X 60 cubic inches (2160 cubic inches...1/10th of a Homer). In ancient England the tub created to measure out a correct bushel volume was described as, "any round measure with a plain and even bottom, being 18.5 inches wide throughout and 8 inches deep". This surviving volume from the old English Winchester Standard, undoubtedly, had a pedigree founded upon older traditions, passed down from distant ancestors.

In the opinion of this researcher, the Winchester bushel represents a "drifted" or "abbreviated" standard from very olden times, inasmuch as the 2150.42 cubic inch volume is completely without meaning, whereas a 2160 cubic inch volume would provide a highly significant value used in astronomy.

This exact description for a bushel (given above) became the volume of the American bushel, which is 2150.42 cubic inches ...derived from the old Winchester Standard and, thankfully, still preserved in the US.

To "unabbreviate" the bushel and return it to its true ancient capacity of 2160 cubic inches, Here's the formula:

10" ÷ (PHI) 1.6180339 = 6.18034".

Now, this increment could be used by all of the cousin nations to create very exact volume vessels of many varying (but perfectly ratioed) capacities. All of those vessels carried a very recognisable capacity code in the cubic inch volume. Let's demonstrate this using the Winchester Standard description as our guide.

By using three of these 6.18034-inch increments to fashion the round base of our tub, the diameter is 18.54102".

This value is a mere .04102" (1/25th of an inch) larger than the Winchester description, but it makes all the difference to precision. Therefore:

The final capacity is: 6.18034 X 3 = 18.54102 inches ÷ 2 = 9.27051 (squared) = 85.94235566 X PI = 270 square inches for the area of the base. We then follow the Winchester standard description and make sides that extend up 8" above the floor of the tub. Therefore the finalised cubic capacity is:

270 square inches X 8 = 2160 cubic inches.

The accurately scaled drawing above shows that 3 true diameters of the Bush Barrow Lozenge artefact perfectly fit within a circle of 18.54102". The Bush Barrow Lozenge was found in a dignitary's barrow-mound grave very close to Stonehenge and within 20-miles of Avebury Henge. It's very probable that the lozenge was used to check the integrity of market place bushel tubs to make sure the general populace was not getting short measures of dry goods from devious merchants.

The same method could be used to create the following ancient capacities:

* 1 Egyptian Theban tub @ 11664 cubic inches could have a base diameter of 18.54102 inches (3 X 6.18034") and sides 43.2 inches high. There would be 270 X 43.2 cubic inches in 11664 cubic inches The length of the Great Pyramid is 432 Hebrew/ Celtic Royal Cubits of 21").

* 1 Greek Metretes vessel @ 2332.8 cubic inches (actually a liquid volume) could have a base diameter of 12.36068 inches (2 X 6.18034") and sides 19.44 inches high. The 19.44 number was used for lunar calculations and the Roman Pace @ 58.32 inches was 3 X 19.44 inches. There would be 120 X 19.44 cubic inches in 2332.8 cubic inches.

* The Hebrew Homer @ 28512 cubic inches could have a base diameter of 30.9017 (5 X 6.18034") and sides that were 38.016 inches high. The number 38.016 is a navigational use number and the Roman Amphora @ 1900.8 cubic inches was 50 X 38.016. Alternatively the Hebrew Homer @ 28512 cubic inches was 750 X 38.016 cubic inches.

* The Roman Amphora @ 1900.8 cubic inches could have a base diameter of 12.36068 inches (2 X 6.18034") and sides 15.84 inches high. The 15.84 number was used in navigation and there would be 120 X 15.84 cubic inches in 1900.8.

* The Babylonian Archane @ 129600 cubic inches could have a base diameter of 49.44272 inches (8 X 6.18034") and sides that extended above the base 67.5 inches. The number 129600 was used in navigation. The sum of 12960 years is half the cycle of the Precession of the Equinoxes. There would be 1920 X 67.5 cubic inches in 129600 cubic inches.

With this very practical application of the PHI reciprocal mathematical formula, the social problem of short measures in the ancient market-places was forever solved. Essentially, this was the ancient formula for "Squaring the Circle" to tolerances that were as close as possible to perfection and the absolute.

Footnote 2.

* The formula used to create the most well-known Egyptian Royal Cubit was: 24883.2-miles of 5250' each = 24741.81818- miles of 5280' ... ÷ 1200 = 20.61818182. This is the published length of the "Royal Cubit" and an exemplar of this size is housed within the Turin Museum. This size also complies to the Great Pyramid's length, which was 440 Egyptian Royal Cubits. Therefore 9072" (756') ÷ 440 = 20.61818182". In other words, using the Egyptian Royal Cubit symbolically to represent "miles" of 5280 feet, this particular cubit represents 1/1200th of the Earth's equatorial circumference under the Great Pyramid's literal base length and height.

* If the Great Pyramid was elongated by 3", then the reading per side would be 756.25' and this system would make the Great Pyramid comply to the ancient British-Germanic Celtic system of navigation under the "11" family of numbers. The inch value for the pyramid's side length would be 9075 and this value ÷ 440 = 20.625". If this cubit was symbolically read as miles, then 1200 of them would give an Earth equatorial circumference of 24750-miles. This value and navigational system was the preferred one adopted and used by many early European mariners. There are 3072 Egyptian Royal Cubits of 20.625" each in the British Standard mile of 5280'.

Amongst the largest of the Egyptian Royal Cubits is one of 20.736" and this one was very special. Whereas viewing the Earth as 24741.81818-miles (literal Great Pyramid standard in miles of 5280') was excellent for navigation using the "6&7" family of numbers, it did not scientifically describe the true size of the Earth. It only provided a very "near" value that was fluidly factorable down to as little as 1-inch or fractions thereof. This close proximity value of the Earth's true dimensions was more than sufficient to ensure safe traversals of the great oceans, using an easily manipulated mathematical system for accurate positional plotting. The British "11" system described the size of the Earth with slightly better accuracy, but was also based upon factored values down to 1-inch or fractions thereof. The most accurate factorable system described the Earth as 12 X 12 X 12 X 12 X 1.2-miles of 5280 feet or 24883.2 British miles (131383296') This value in miles (24883.2) ÷ 1200 = 20.736.

Sir William Flinders Petrie measured the coffer in the Great Chamber of the Khafre Pyramid and accurately determined it had an outer length of 103.68"* (this was the "mean" after 3 length measurements of top, mid and base). This value doubled = 207.36" (2079/25ths). In other words, the coffer was 5 cubits long using a cubit of 20.736" or 1.728'. The same cubit was represented in the dimensions of paving slabs at the base of the Great Pyramid. One of several codes carried in the length value of the coffer was the speed at which the Earth rotates in miles per hour. Therefore: 24883.2-miles ÷ 24-hours = 1036.8 MPH. Interestingly enough, the "Stirling Jug" of Scotland had a capacity of 103.68 cubic inches and this paralleled the Jerusalem Liquid Standard of the ancient Hebrews (no relationship to the present-day people calling themselves Jewish or Jews), wherein a "Cab" was 103.68-cubic inches. The value of 24883.2-miles to describe the Earth's equatorial size is in deficit error of only 18.8-miles.

*For Petrie's measurements of the Khafre Pyramid coffer see: The Pyramids and Temples of Gizeh, by Sir Flinders Petrie, Chpt. 9, Section 77, available online @

Each of the Egyptian Royal Cubits, beside coding equatorial circumference of the Earth measurements according to three separate systems, also coded the speed at which the Earth rotates. To get the equatorial speed of rotation under each system, simply halve the inch value of the cubit under consideration and multiply by 100, then read the value acquired as MPH. The true rotational speed is very close to 1037.583333 MPH (10377/12ths), so a reading of 1036.8 MPH is only off by .783333 MPH.

The segments of an Egyptian Royal Cubit of 20.618" in length (as displayed at the Turin museum). The 1st interval is a PHI inch (1-inch X 1.6180339); The 2nd interval is a PI inch (1-inch X 3.1416); The 3rd interval seems to be coded at 4.6656 / 4.6666" (related to the "so-called" Roman foot of 11.664 / 11.666"); The 4th interval is a special PHI reciprocal value that was absolutely essential for the fabrication of correct (precise capacity) round volume vessels for the ancient market places. The 5th interval is navigational (note: the Great Pyramid is 756' long), etc.
The Royal Cubit layout seems to have been unsuitable as a rule used in building work, but functioned more as a specialised calculator and memory device. Other, more factorable, cubit or foot rules would have been used in construction work.